Question

True or false The function $f\left(x\right)=\sqrt{x}$is even.

Short answer

The statement "The function$f\left(x\right)=\sqrt{x}$is even" is false.

Step-by-step solution

Step 1. Given information.

We have:

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

Step 2. Find whether the statement is true or false.

Even function: A function is even if $f\left(-x\right)=f\left(x\right)$for all $x\in R$.

Substitute $x=-x$:

$$\begin{gathered} f\left(x\right)=\sqrt{x} \\ f(-x)=\sqrt{-x} \\ \Rightarrow f\left(x\right)\ne f(-x) \end{gathered}$$

Therefore, $f\left(x\right)=\sqrt{x}$is not even function.