Precalculus Examples

$f (x) = - \sqrt{2 x}$

Step 1

Find $f (- x)$ .

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Step 1.1

Find $f (- x)$ by substituting $- x$ for all occurrence of $x$ in $f (x)$ .

$f (- x) = - \sqrt{2 (- x)}$

Step 1.2

Multiply $- 1$ by $2$ .

$f (- x) = - \sqrt{- 2 x}$

Step 2

A function is even if $f (- x) = f (x)$ .

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Step 2.1

Check if $f (- x) = f (x)$ .

Step 2.2

Since $- \sqrt{- 2 x}$ $\neq$ $- \sqrt{2 x}$ , the function is not even.

The function is not even

Step 3

A function is odd if $f (- x) = - f (x)$ .

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Step 3.1

Multiply $- (- \sqrt{2 x})$ .

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Step 3.1.1

Multiply $- 1$ by $- 1$ .

$- f (x) = 1 \sqrt{2 x}$

Step 3.1.2

Multiply $\sqrt{2 x}$ by $1$ .

$- f (x) = \sqrt{2 x}$

Step 3.2

Since $- \sqrt{- 2 x}$ $\neq$ $\sqrt{2 x}$ , the function is not odd.

The function is not odd

Step 4

The function is neither odd nor even

Step 5