Question

How do you know if `f(x) = (x^2+8)^2` is an even or odd function?

Answer 1

`f(x)=(x^2+8)^2` is even and not odd

Explanation:

even functions
A function `f(x)` is even `hArr f(x)=f(-x) AAx`

For the specific case of `f(x)=(x^2+8)^2`
`color(white)("XXX")f(-x) = ((-x)^2+8)^2`
`color(white)("XXXXXXX")=(x^2+8)^2`
`color(white)("XXXXXXX")=f(x)`

So the function is even

`bar(color(white)("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX"))`

odd functions
A function `f(x)` is odd `hArr f(-x)=-f(x) AAx`

For the specific case of `f(x)=(x^2+8)^2`
`color(white)("XXX")f(-x) (=f(x)) > 0 AAx`
Therefore
`color(white)("XXX")-f(x) < 0 AAx`

`f(-x) != -f(x)`

So the function is not odd