Q.38 - Precalculus Enhanced with Graphing Utilities

Question

Determine algebraically whether each function is even, odd, or neither.

$G\left(x\right)=\sqrt{x}$

Step-by-Step Solution

Answer

$G\left(x\right)$ is neither even nor odd function.

Step 1: Given information.

The function, $G\left(x\right)=\sqrt{x}$.

Step 2: Write definition of even function and odd function.

• A function $f\left(x\right)$ is said to be an even function if $f\left(-x\right)=f\left(x\right)$.
• A function is said to be an odd function if $f\left(-x\right)=-f\left(x\right)$.

Step 3: Calculate G - x .

Replace $x$ by $-x$ into the given function $G\left(x\right)=\sqrt{x}$.

$G\left(-x\right)=\sqrt{-x}$

Clearly, $G\left(-x\right)\ne G\left(x\right) and G\left(-x\right)\ne -G\left(x\right)$

So by definition, $G\left(x\right)$ is neither even nor odd function.