Chapter 3, Problem 12CR

Is the function $f(x)=\frac{x^2}{2x+1}$ even, odd, or neither?

To determine

To calculate: If the given function $f(x)=\frac{x^2}{2x+1}$ is even, odd or neither.

Answer to Problem 12CR

Solution:

The given function is neither even nor odd.

Explanation of Solution

Given:

The given function is $f(x)=\frac{x^2}{2x+1}$.

Formula used:

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

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

Calculation:

We have $f(x)=\frac{x^2}{2x+1}$.

$f(-x)=\frac{{(-x)}^2}{2(-x)+1}=\frac{x^2}{-2x+1}$

Here, we can see that the given function is neither even nor odd.