Trigonometry Examples

$f (x) = \frac{x - 7}{x^{3} + 1}$ , $f (x) = 2$

Step 1

Substitute $2$ for $f (x)$ .

$2 = \frac{x - 7}{x^{3} + 1}$

Step 2

Solve for $x$ .

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Step 2.1

Simplify the denominator.

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Step 2.1.1

Rewrite $1$ as $1^{3}$ .

$2 = \frac{x - 7}{x^{3} + 1^{3}}$

Step 2.1.2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = x$ and $b = 1$ .

$2 = \frac{x - 7}{(x + 1) (x^{2} - x \cdot 1 + 1^{2})}$

Step 2.1.3

Simplify.

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Step 2.1.3.1

Multiply $- 1$ by $1$ .

$2 = \frac{x - 7}{(x + 1) (x^{2} - x + 1^{2})}$

Step 2.1.3.2

One to any power is one.

$2 = \frac{x - 7}{(x + 1) (x^{2} - x + 1)}$

Step 2.2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 1.7517966$

Step 3