Calculus Examples

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

Step 1

Replace the variable $x$ with $4$ in the expression.

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

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

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

Step 2.1.2

Raise $4$ to the power of $2$ .

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

Step 2.1.3

Cancel the common factor of $4$ .

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Step 2.1.3.1

Factor $4$ out of $- 4$ .

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

Step 2.1.3.2

Factor $4$ out of $16$ .

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

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.

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

Step 2.1.4

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

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

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 $4$ .

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

Step 2.3

The final answer is $\frac{3}{4}$ .

$\frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$

Step 4