Chapter 13.5, Problem 5ST

a.

To determine

If the given function is odd or even or neither.

Explanation of Solution

Given information:

The given function is $f(x)=x^4-3x^2+5$

Calculations:

Here the given function is $f(x)=x^4-3x^2+5$ .

Now a function is said to be a odd function if

  $f(-x)=-f(x)$

Also a function is said to be even function if,

  $f(-x)=f(x)$

Now,

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

Therefore the given function is an even function.

b.

To determine

If the given function is odd or even or neither.

Explanation of Solution

Given information:

The given function is $g(x)=2x^2+6x+4$

Calculations:

Here the given function is $g(x)=2x^2+6x+4$ .

Now a function is said to be a odd function if

  $f(-x)=-f(x)$

Also a function is said to be even function if,

  $f(-x)=f(x)$

Now,

  $\begin{array}{l}g(x)=2x^2+6x+4\\ g(-x)=2{(}^{-}+6(-x)+4\\ g(-x)=2x^2-6x+4\\ g(-x)\ne g(x)\ne -g(x)\end{array}$

Therefore the given function is neither odd function nor an even function.