Chapter 13.3, Problem 17WE

To determine

To find:Whether the function is even, odd or neither.

Answer to Problem 17WE

The function is even.

Explanation of Solution

Given information: The function is $f\left(x\right)=x\sin x$

Calculation:

Consider the function.

  $f\left(x\right)=x\sin x$

Substitute $x=-x$ in above function.

  $\begin{array}{l}f\left(-x\right)=\left(-x\right)\sin \left(-x\right)\\ f\left(-x\right)=x\sin x\\ f\left(-x\right)=f\left(x\right)\end{array}$

Thus, the function is even.