Calculus Examples

$f (x) = \frac{1}{\sqrt{x}}$ , $x = \frac{1}{16}$

Step 1

Replace the variable $x$ with $\frac{1}{16}$ in the expression.

$f (\frac{1}{16}) = \frac{1}{\sqrt{\frac{1}{16}}}$

Step 2

Simplify the result.

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Step 2.1

Remove parentheses.

$f (\frac{1}{16}) = \frac{1}{\sqrt{\frac{1}{16}}}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Rewrite $\sqrt{\frac{1}{16}}$ as $\frac{\sqrt{1}}{\sqrt{16}}$ .

$f (\frac{1}{16}) = \frac{1}{\frac{\sqrt{1}}{\sqrt{16}}}$

Step 2.2.2

Any root of $1$ is $1$ .

$f (\frac{1}{16}) = \frac{1}{\frac{1}{\sqrt{16}}}$

Step 2.2.3

Simplify the denominator.

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Step 2.2.3.1

Rewrite $16$ as $4^{2}$ .

$f (\frac{1}{16}) = \frac{1}{\frac{1}{\sqrt{4^{2}}}}$

Step 2.2.3.2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 2.3

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.4

Multiply $4$ by $1$ .

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

Step 2.5

The final answer is $4$ .

$4$

Step 3