Chapter 13.3, Problem 5OE

To determine

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

Answer to Problem 5OE

The function is even.

Explanation of Solution

Given information: The function is $h\left(x\right)=2x^4-3x^2+5$

Calculation:

Consider the function.

  $h\left(x\right)=2x^4-3x^2+5$

  $g\left(x\right)=2x^3-3x$

Substitute $x=-x$ in above function.

  $\begin{array}{l}h\left(-x\right)=2{\left(-x\right)}^4-3{\left(-x\right)}^2+5\\ h\left(-x\right)=2x^4-3x^2+5\\ h\left(-x\right)=h\left(x\right)\end{array}$

Thus, the function is even.