Question

If $g\left(x\right)=x^2+x-2$, which of the following is true?

• A. $g\left(x\right)$ is neither even nor odd.
• B. $g\left(x\right)$ is even.
• C. $g\left(x\right)$ is odd.
• D. $[-g(x\left)\right]=g\left(x\right)$

Answer 1

Answer: (A)

$g\left(x\right)$ is neither even nor odd.

$g\left(x\right)=x^2+x-2g(-x)={(-x)}^2+(-x)-2\Rightarrow g(-x)=x-x-2\Rightarrow g\left(x\right)\ne -g\left(x\right)\Rightarrow g\left(x\right)\ne g(-x)$

Therefore $g\left(x\right)$ is neither even nor odd

Option $A$ is correct.