Trigonometry Examples

$\frac{4}{49} - \frac{4}{7 x} \div \frac{x}{49} - \frac{1}{x}$

Step 1

Interchange the variables.

$x = \frac{4}{49} - \frac{4}{7 y} \div \frac{y}{49} - \frac{1}{y}$

Step 2

Solve for $y$ .

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Step 2.1

Rewrite the equation as $\frac{4}{49} - \frac{4}{7 y} \div \frac{y}{49} - \frac{1}{y} = x$ .

$\frac{4}{49} - \frac{4}{7 y} \div \frac{y}{49} - \frac{1}{y} = x$

Step 2.2

Factor each term.

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Step 2.2.1

To divide by a fraction, multiply by its reciprocal.

$\frac{4}{49} - (\frac{4}{7 y} \cdot \frac{49}{y}) - \frac{1}{y} = x$

Step 2.2.2

Cancel the common factor of $7$ .

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Step 2.2.2.1

Factor $7$ out of $7 y$ .

$\frac{4}{49} - (\frac{4}{7 (y)} \cdot \frac{49}{y}) - \frac{1}{y} = x$

Step 2.2.2.2

Factor $7$ out of $49$ .

$\frac{4}{49} - (\frac{4}{7 (y)} \cdot \frac{7 (7)}{y}) - \frac{1}{y} = x$

Step 2.2.2.3

Cancel the common factor.

$\frac{4}{49} - (\frac{4}{7 y} \cdot \frac{7 \cdot 7}{y}) - \frac{1}{y} = x$

Step 2.2.2.4

Rewrite the expression.

$\frac{4}{49} - (\frac{4}{y} \cdot \frac{7}{y}) - \frac{1}{y} = x$

Step 2.2.3

Multiply $\frac{4}{y}$ by $\frac{7}{y}$ .

$\frac{4}{49} - \frac{4 \cdot 7}{y \cdot y} - \frac{1}{y} = x$

Step 2.2.4

Multiply $4$ by $7$ .

$\frac{4}{49} - \frac{28}{y \cdot y} - \frac{1}{y} = x$

Step 2.2.5

Raise $y$ to the power of $1$ .

$\frac{4}{49} - \frac{28}{y^{1} y} - \frac{1}{y} = x$

Step 2.2.6

Raise $y$ to the power of $1$ .

$\frac{4}{49} - \frac{28}{y^{1} y^{1}} - \frac{1}{y} = x$

Step 2.2.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{49} - \frac{28}{y^{1 + 1}} - \frac{1}{y} = x$

Step 2.2.8

Add $1$ and $1$ .

$\frac{4}{49} - \frac{28}{y^{2}} - \frac{1}{y} = x$

Step 2.3

Find the LCD of the terms in the equation.

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Step 2.3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$49, y^{2}, y, 1$

Step 2.3.2

Since $49, y^{2}, y, 1$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $49, 1, 1, 1$ then find LCM for the variable part $y^{2}, y^{1}$ .

Step 2.3.3

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Step 2.3.4

$49$ has factors of $7$ and $7$ .

$7 \cdot 7$

Step 2.3.5

The number $1$ is not a prime number because it only has one positive factor, which is itself.

Not prime

Step 2.3.6

The LCM of $49, 1, 1, 1$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$7 \cdot 7$

Step 2.3.7

Multiply $7$ by $7$ .

$49$

Step 2.3.8

The factors for $y^{2}$ are $y \cdot y$ , which is $y$ multiplied by each other $2$ times.

$y^{2} = y \cdot y$

$y$ occurs $2$ times.

Step 2.3.9

The factor for $y^{1}$ is $y$ itself.

$y^{1} = y$

$y$ occurs $1$ time.

Step 2.3.10

The LCM of $y^{2}, y^{1}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

$y \cdot y$

Step 2.3.11

Multiply $y$ by $y$ .

$y^{2}$

Step 2.3.12

The LCM for $49, y^{2}, y, 1$ is the numeric part $49$ multiplied by the variable part.

$49 y^{2}$

Step 2.4

Multiply each term in $\frac{4}{49} - \frac{28}{y^{2}} - \frac{1}{y} = x$ by $49 y^{2}$ to eliminate the fractions.

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Step 2.4.1

Multiply each term in $\frac{4}{49} - \frac{28}{y^{2}} - \frac{1}{y} = x$ by $49 y^{2}$ .

$\frac{4}{49} (49 y^{2}) - \frac{28}{y^{2}} (49 y^{2}) - \frac{1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Simplify each term.

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Step 2.4.2.1.1

Cancel the common factor of $49$ .

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Step 2.4.2.1.1.1

Factor $49$ out of $49 y^{2}$ .

$\frac{4}{49} (49 (y^{2})) - \frac{28}{y^{2}} (49 y^{2}) - \frac{1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2.1.1.2

Cancel the common factor.

$\frac{4}{49} (49 y^{2}) - \frac{28}{y^{2}} (49 y^{2}) - \frac{1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2.1.1.3

Rewrite the expression.

$4 y^{2} - \frac{28}{y^{2}} (49 y^{2}) - \frac{1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2.1.2

Cancel the common factor of $y^{2}$ .

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Step 2.4.2.1.2.1

Move the leading negative in $- \frac{28}{y^{2}}$ into the numerator.

$4 y^{2} + \frac{- 28}{y^{2}} (49 y^{2}) - \frac{1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2.1.2.2

Factor $y^{2}$ out of $49 y^{2}$ .

$4 y^{2} + \frac{- 28}{y^{2}} (y^{2} \cdot 49) - \frac{1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2.1.2.3

Cancel the common factor.

$4 y^{2} + \frac{- 28}{y^{2}} (y^{2} \cdot 49) - \frac{1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2.1.2.4

Rewrite the expression.

$4 y^{2} - 28 \cdot 49 - \frac{1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2.1.3

Multiply $- 28$ by $49$ .

$4 y^{2} - 1372 - \frac{1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2.1.4

Cancel the common factor of $y$ .

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Step 2.4.2.1.4.1

Move the leading negative in $- \frac{1}{y}$ into the numerator.

$4 y^{2} - 1372 + \frac{- 1}{y} (49 y^{2}) = x (49 y^{2})$

Step 2.4.2.1.4.2

Factor $y$ out of $49 y^{2}$ .

$4 y^{2} - 1372 + \frac{- 1}{y} (y (49 y)) = x (49 y^{2})$

Step 2.4.2.1.4.3

Cancel the common factor.

$4 y^{2} - 1372 + \frac{- 1}{y} (y (49 y)) = x (49 y^{2})$

Step 2.4.2.1.4.4

Rewrite the expression.

$4 y^{2} - 1372 - (49 y) = x (49 y^{2})$

Step 2.4.2.1.5

Multiply $49$ by $- 1$ .

$4 y^{2} - 1372 - 49 y = x (49 y^{2})$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Rewrite using the commutative property of multiplication.

$4 y^{2} - 1372 - 49 y = 49 x y^{2}$

Step 2.5

Solve the equation.

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Step 2.5.1

Subtract $49 x y^{2}$ from both sides of the equation.

$4 y^{2} - 1372 - 49 y - 49 x y^{2} = 0$

Step 2.5.2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2.5.3

Substitute the values $a = 4 - 49 x$ , $b = - 49$ , and $c = - 1372$ into the quadratic formula and solve for $y$ .

$\frac{49 \pm \sqrt{{(- 49)}^{2} - 4 \cdot ((4 - 49 x) \cdot - 1372)}}{2 (4 - 49 x)}$

Step 2.5.4

Simplify the numerator.

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Step 2.5.4.1

Raise $- 49$ to the power of $2$ .

$y = \frac{49 \pm \sqrt{2401 - 4 \cdot (4 - 49 x) \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.4.2

Apply the distributive property.

$y = \frac{49 \pm \sqrt{2401 + (- 4 \cdot 4 - 4 (- 49 x)) \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.4.3

Multiply $- 4$ by $4$ .

$y = \frac{49 \pm \sqrt{2401 + (- 16 - 4 (- 49 x)) \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.4.4

Multiply $- 49$ by $- 4$ .

$y = \frac{49 \pm \sqrt{2401 + (- 16 + 196 x) \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.4.5

Apply the distributive property.

$y = \frac{49 \pm \sqrt{2401 - 16 \cdot - 1372 + 196 x \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.4.6

Multiply $- 16$ by $- 1372$ .

$y = \frac{49 \pm \sqrt{2401 + 21952 + 196 x \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.4.7

Multiply $- 1372$ by $196$ .

$y = \frac{49 \pm \sqrt{2401 + 21952 - 268912 x}}{2 (4 - 49 x)}$

Step 2.5.4.8

Add $2401$ and $21952$ .

$y = \frac{49 \pm \sqrt{24353 - 268912 x}}{2 (4 - 49 x)}$

Step 2.5.4.9

Factor $343$ out of $24353 - 268912 x$ .

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Step 2.5.4.9.1

Factor $343$ out of $24353$ .

$y = \frac{49 \pm \sqrt{343 (71) - 268912 x}}{2 (4 - 49 x)}$

Step 2.5.4.9.2

Factor $343$ out of $- 268912 x$ .

$y = \frac{49 \pm \sqrt{343 (71) + 343 (- 784 x)}}{2 (4 - 49 x)}$

Step 2.5.4.9.3

Factor $343$ out of $343 (71) + 343 (- 784 x)$ .

$y = \frac{49 \pm \sqrt{343 (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.4.10

Rewrite $343 (71 - 784 x)$ as $7^{2} \cdot (7 (71 - 784 x))$ .

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Step 2.5.4.10.1

Factor $49$ out of $343$ .

$y = \frac{49 \pm \sqrt{49 (7) (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.4.10.2

Rewrite $49$ as $7^{2}$ .

$y = \frac{49 \pm \sqrt{7^{2} \cdot (7 (71 - 784 x))}}{2 (4 - 49 x)}$

Step 2.5.4.10.3

Add parentheses.

$y = \frac{49 \pm \sqrt{7^{2} \cdot (7 (71 - 784 x))}}{2 (4 - 49 x)}$

Step 2.5.4.11

Pull terms out from under the radical.

$y = \frac{49 \pm 7 \sqrt{7 (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.5

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Step 2.5.5.1

Change the $\pm$ to $+$ .

$y = \frac{49 + 7 \sqrt{7 (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.5.2

Factor $7$ out of $49 + 7 \sqrt{7 (71 - 784 x)}$ .

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Step 2.5.5.2.1

Factor $7$ out of $49$ .

$y = \frac{7 \cdot 7 + 7 \sqrt{7 (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.5.2.2

Factor $7$ out of $7 \cdot 7 + 7 \sqrt{7 (71 - 784 x)}$ .

$y = \frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

Step 2.5.6

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Step 2.5.6.1

Simplify the numerator.

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Step 2.5.6.1.1

Raise $- 49$ to the power of $2$ .

$y = \frac{49 \pm \sqrt{2401 - 4 \cdot (4 - 49 x) \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.6.1.2

Apply the distributive property.

$y = \frac{49 \pm \sqrt{2401 + (- 4 \cdot 4 - 4 (- 49 x)) \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.6.1.3

Multiply $- 4$ by $4$ .

$y = \frac{49 \pm \sqrt{2401 + (- 16 - 4 (- 49 x)) \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.6.1.4

Multiply $- 49$ by $- 4$ .

$y = \frac{49 \pm \sqrt{2401 + (- 16 + 196 x) \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.6.1.5

Apply the distributive property.

$y = \frac{49 \pm \sqrt{2401 - 16 \cdot - 1372 + 196 x \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.6.1.6

Multiply $- 16$ by $- 1372$ .

$y = \frac{49 \pm \sqrt{2401 + 21952 + 196 x \cdot - 1372}}{2 (4 - 49 x)}$

Step 2.5.6.1.7

Multiply $- 1372$ by $196$ .

$y = \frac{49 \pm \sqrt{2401 + 21952 - 268912 x}}{2 (4 - 49 x)}$

Step 2.5.6.1.8

Add $2401$ and $21952$ .

$y = \frac{49 \pm \sqrt{24353 - 268912 x}}{2 (4 - 49 x)}$

Step 2.5.6.1.9

Factor $343$ out of $24353 - 268912 x$ .

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Step 2.5.6.1.9.1

Factor $343$ out of $24353$ .

$y = \frac{49 \pm \sqrt{343 (71) - 268912 x}}{2 (4 - 49 x)}$

Step 2.5.6.1.9.2

Factor $343$ out of $- 268912 x$ .

$y = \frac{49 \pm \sqrt{343 (71) + 343 (- 784 x)}}{2 (4 - 49 x)}$

Step 2.5.6.1.9.3

Factor $343$ out of $343 (71) + 343 (- 784 x)$ .

$y = \frac{49 \pm \sqrt{343 (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.6.1.10

Rewrite $343 (71 - 784 x)$ as $7^{2} \cdot (7 (71 - 784 x))$ .

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Step 2.5.6.1.10.1

Factor $49$ out of $343$ .

$y = \frac{49 \pm \sqrt{49 (7) (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.6.1.10.2

Rewrite $49$ as $7^{2}$ .

$y = \frac{49 \pm \sqrt{7^{2} \cdot (7 (71 - 784 x))}}{2 (4 - 49 x)}$

Step 2.5.6.1.10.3

Add parentheses.

$y = \frac{49 \pm \sqrt{7^{2} \cdot (7 (71 - 784 x))}}{2 (4 - 49 x)}$

Step 2.5.6.1.11

Pull terms out from under the radical.

$y = \frac{49 \pm 7 \sqrt{7 (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.6.2

Change the $\pm$ to $-$ .

$y = \frac{49 - 7 \sqrt{7 (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.6.3

Factor $7$ out of $49 - 7 \sqrt{7 (71 - 784 x)}$ .

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Step 2.5.6.3.1

Factor $7$ out of $49$ .

$y = \frac{7 (7) - 7 \sqrt{7 (71 - 784 x)}}{2 (4 - 49 x)}$

Step 2.5.6.3.2

Factor $7$ out of $- 7 \sqrt{7 (71 - 784 x)}$ .

$y = \frac{7 (7) + 7 (- \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

Step 2.5.6.3.3

Factor $7$ out of $7 (7) + 7 (- \sqrt{7 (71 - 784 x)})$ .

$y = \frac{7 (7 - \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

Step 2.5.7

The final answer is the combination of both solutions.

$y = \frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

$y = \frac{7 (7 - \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

$y = \frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

$y = \frac{7 (7 - \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

$y = \frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

$y = \frac{7 (7 - \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

Step 3

Replace $y$ with $f^{- 1} (x)$ to show the final answer.

$f^{- 1} (x) = \frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}, \frac{7 (7 - \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$

Step 4

Verify if $f^{- 1} (x) = \frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}, \frac{7 (7 - \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$ is the inverse of $f (x) = \frac{4}{49} - \frac{4}{7 x} \div \frac{x}{49} - \frac{1}{x}$ .

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Step 4.1

The domain of the inverse is the range of the original function and vice versa. Find the domain and the range of $f (x) = \frac{4}{49} - \frac{4}{7 x} \div \frac{x}{49} - \frac{1}{x}$ and $f^{- 1} (x) = \frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}, \frac{7 (7 - \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$ and compare them.

Step 4.2

Find the range of $f (x) = \frac{4}{49} - \frac{4}{7 x} \div \frac{x}{49} - \frac{1}{x}$ .

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Step 4.2.1

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \frac{71}{784}]$

Step 4.3

Find the domain of $\frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$ .

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Step 4.3.1

Set the radicand in $\sqrt{7 (71 - 784 x)}$ greater than or equal to $0$ to find where the expression is defined.

$7 (71 - 784 x) \geq 0$

Step 4.3.2

Solve for $x$ .

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Step 4.3.2.1

Divide each term in $7 (71 - 784 x) \geq 0$ by $7$ and simplify.

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Step 4.3.2.1.1

Divide each term in $7 (71 - 784 x) \geq 0$ by $7$ .

$\frac{7 (71 - 784 x)}{7} \geq \frac{0}{7}$

Step 4.3.2.1.2

Simplify the left side.

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Step 4.3.2.1.2.1

Cancel the common factor of $7$ .

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Step 4.3.2.1.2.1.1

Cancel the common factor.

$\frac{7 (71 - 784 x)}{7} \geq \frac{0}{7}$

Step 4.3.2.1.2.1.2

Divide $71 - 784 x$ by $1$ .

$71 - 784 x \geq \frac{0}{7}$

Step 4.3.2.1.3

Simplify the right side.

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Step 4.3.2.1.3.1

Divide $0$ by $7$ .

$71 - 784 x \geq 0$

Step 4.3.2.2

Subtract $71$ from both sides of the inequality.

$- 784 x \geq - 71$

Step 4.3.2.3

Divide each term in $- 784 x \geq - 71$ by $- 784$ and simplify.

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Step 4.3.2.3.1

Divide each term in $- 784 x \geq - 71$ by $- 784$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 784 x}{- 784} \leq \frac{- 71}{- 784}$

Step 4.3.2.3.2

Simplify the left side.

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Step 4.3.2.3.2.1

Cancel the common factor of $- 784$ .

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Step 4.3.2.3.2.1.1

Cancel the common factor.

$\frac{- 784 x}{- 784} \leq \frac{- 71}{- 784}$

Step 4.3.2.3.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 71}{- 784}$

Step 4.3.2.3.3

Simplify the right side.

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Step 4.3.2.3.3.1

Dividing two negative values results in a positive value.

$x \leq \frac{71}{784}$

Step 4.3.3

Set the denominator in $\frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$ equal to $0$ to find where the expression is undefined.

$2 (4 - 49 x) = 0$

Step 4.3.4

Solve for $x$ .

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Step 4.3.4.1

Divide each term in $2 (4 - 49 x) = 0$ by $2$ and simplify.

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Step 4.3.4.1.1

Divide each term in $2 (4 - 49 x) = 0$ by $2$ .

$\frac{2 (4 - 49 x)}{2} = \frac{0}{2}$

Step 4.3.4.1.2

Simplify the left side.

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Step 4.3.4.1.2.1

Cancel the common factor of $2$ .

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Step 4.3.4.1.2.1.1

Cancel the common factor.

$\frac{2 (4 - 49 x)}{2} = \frac{0}{2}$

Step 4.3.4.1.2.1.2

Divide $4 - 49 x$ by $1$ .

$4 - 49 x = \frac{0}{2}$

Step 4.3.4.1.3

Simplify the right side.

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Step 4.3.4.1.3.1

Divide $0$ by $2$ .

$4 - 49 x = 0$

Step 4.3.4.2

Subtract $4$ from both sides of the equation.

$- 49 x = - 4$

Step 4.3.4.3

Divide each term in $- 49 x = - 4$ by $- 49$ and simplify.

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Step 4.3.4.3.1

Divide each term in $- 49 x = - 4$ by $- 49$ .

$\frac{- 49 x}{- 49} = \frac{- 4}{- 49}$

Step 4.3.4.3.2

Simplify the left side.

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Step 4.3.4.3.2.1

Cancel the common factor of $- 49$ .

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Step 4.3.4.3.2.1.1

Cancel the common factor.

$\frac{- 49 x}{- 49} = \frac{- 4}{- 49}$

Step 4.3.4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 49}$

Step 4.3.4.3.3

Simplify the right side.

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Step 4.3.4.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{4}{49}$

Step 4.3.5

The domain is all values of $x$ that make the expression defined.

$(- \infty, \frac{4}{49}) \cup (\frac{4}{49}, \frac{71}{784}]$

Step 4.4

Since the domain of $f^{- 1} (x) = \frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}, \frac{7 (7 - \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$ is not equal to the range of $f (x) = \frac{4}{49} - \frac{4}{7 x} \div \frac{x}{49} - \frac{1}{x}$ , then $f^{- 1} (x) = \frac{7 (7 + \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}, \frac{7 (7 - \sqrt{7 (71 - 784 x)})}{2 (4 - 49 x)}$ is not an inverse of $f (x) = \frac{4}{49} - \frac{4}{7 x} \div \frac{x}{49} - \frac{1}{x}$ .

There is no inverse

Step 5