Chapter 1, Problem 19RE

To determine

To check: Whether the function $y=x^2+1$ is even, odd or neither.

Answer to Problem 19RE

The function $y=x^2+1$ is an even function.

Explanation of Solution

Given information: The given function is $y=x^2+1$ .

Calculation:

Even function: A function $f\left(x\right)$ is said to be an even function if it satisfies the condition $f\left(-x\right)=f\left(x\right)$ .

Odd function: A function $f\left(x\right)$ is said to be an odd function if it satisfies the condition $f\left(-x\right)=-f\left(x\right)$ .

Substitute $-x$ for $x$ in the given function $y=f\left(x\right)=x^2+1$ .

  $\begin{array}{c}f\left(-x\right)={\left(-x\right)}^2+1\\ =x^2+1\\ =f\left(x\right)\end{array}$

Therefore, the function $y=x^2+1$ is an even function.