Calculus Examples

f (4) = 1 - 4 x^{- 2}

$f (4) = 1 - 4 x^{- 2}$

Step 1

Replace the variable

x

$x$ with

4

$4$ in the expression.

f (4) = 1 - 4 {(4)}^{- 2}

$f (4) = 1 - 4 {(4)}^{- 2}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

f (4) = 1 - 4 \frac{1}{4^{2}}

$f (4) = 1 - 4 \frac{1}{4^{2}}$

Step 2.1.2

Raise

4

$4$ to the power of

2

$2$ .

f (4) = 1 - 4 (\frac{1}{16})

$f (4) = 1 - 4 (\frac{1}{16})$

Step 2.1.3

Cancel the common factor of

4

$4$ .

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Step 2.1.3.1

Factor

4

$4$ out of

- 4

$- 4$ .

f (4) = 1 + 4 (- 1) (\frac{1}{16})

$f (4) = 1 + 4 (- 1) (\frac{1}{16})$

Step 2.1.3.2

Factor

4

$4$ out of

16

$16$ .

f (4) = 1 + 4 \cdot (- 1 \frac{1}{4 \cdot 4})

$f (4) = 1 + 4 \cdot (- 1 \frac{1}{4 \cdot 4})$

Step 2.1.3.3

Cancel the common factor.

$f (4) = 1 + 4 \cdot (- 1 \frac{1}{4 \cdot 4})$

Step 2.1.3.4

Rewrite the expression.

$f (4) = 1 - 1 (\frac{1}{4})$

$f (4) = 1 - 1 (\frac{1}{4})$

Step 2.1.4

Rewrite

$- 1 (\frac{1}{4})$ as

$- (\frac{1}{4})$ .

$f (4) = 1 - \frac{1}{4}$

$f (4) = 1 - \frac{1}{4}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

$f (4) = \frac{4}{4} - \frac{1}{4}$

Step 2.2.2

Combine the numerators over the common denominator.

$f (4) = \frac{4 - 1}{4}$

Step 2.2.3

Subtract

$1$ from

$4$ .

$f (4) = \frac{3}{4}$

$f (4) = \frac{3}{4}$

Step 2.3

The final answer is

$\frac{3}{4}$ .

$\frac{3}{4}$

$\frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$

Step 4

$f (4) = 1 - 4 x^{- 2}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$