Question

How do you determine if `h(x)= x^4+3x^2` is an even or odd function?

Answer 1

`h(x)` is an even function.

Explanation:

A function`h(x)` is even if `h(x)=h(-x)`

and it is odd if `h(x)=-h(-x)`

As `h(x)=x^4+3x^2`

`h(-x)=(-x)^4+3(-x)^2`

= `(-1)^4xx x^4+3xx(-1)^2xx x^2`

= `1xxx^4+3xx1xxx^2`

= `x^4+3x^2`

= `h(x)`

Hence `h(x)` is an even function.