Chapter 2, Problem 20RE

To determine

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

Answer to Problem 20RE

Solution:

Neither.

Explanation of Solution

Given:

$G\left(x\right)=1-x+x^3$

Formula used:

A function is even if $f\left(-x\right)=f(x)$.

A function is odd if $f\left(-x\right)=-f(x)$.

Calculation:

$G\left(x\right)=1-x+x^3$

$G\left(-x\right)=1-\left(-x\right)+{\left(-x\right)}^3)$

$G\left(-x\right)=1+x-x^3$

$G\left(-x\right)\ne G\left(x\right)$

$G\left(-x\right)\ne -G\left(x\right)$

Therefore, the function is neither even nor odd.