Determine if Odd, Even, or Neither square root of 3x

$\sqrt{3 x}$

Step 1

Write $\sqrt{3 x}$ as a function.

$f (x) = \sqrt{3 x}$

Step 2

Find $f (- x)$ .

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

$f (- x) = \sqrt{3 (- x)}$

Multiply $- 1$ by $3$ .

$f (- x) = \sqrt{- 3 x}$

Step 3

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

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

$\sqrt{- 3 x}$ $\neq$ $\sqrt{3 x}$

Since $\sqrt{- 3 x}$ $\neq$ $\sqrt{3 x}$ , the function is not even.

The function is not even

Step 4

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

Multiply $- 1$ by $\sqrt{3 x}$ .

$- f (x) = - \sqrt{3 x}$

Since $\sqrt{- 3 x}$ $\neq$ $- \sqrt{3 x}$ , the function is not odd.

The function is not odd

Step 5

The function is neither odd nor even

Step 6