Algebra Examples

$\sqrt{8 x}$

Step 1

Write $\sqrt{8 x}$ as a function.

$f (x) = \sqrt{8 x}$

Step 2

Simplify.

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Step 2.1

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

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Step 2.1.1

Factor $4$ out of $8$ .

$f (x) = \sqrt{4 (2) x}$

Step 2.1.2

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

$f (x) = \sqrt{2^{2} \cdot (2 x)}$

Step 2.1.3

Add parentheses.

$f (x) = \sqrt{2^{2} \cdot (2 x)}$

Step 2.2

Pull terms out from under the radical.

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

Step 3

Find $f (- x)$ .

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Step 3.1

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

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

Step 3.2

Multiply $- 1$ by $2$ .

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

Step 4

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

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Step 4.1

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

Step 4.2

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

The function is not even

Step 5

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

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Step 5.1

Multiply $2$ by $- 1$ .

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

Step 5.2

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

The function is not odd

Step 6

The function is neither odd nor even

Step 7