Question

Which functions are even? Check all of the boxes that apply.f(x)=x4+ - x2?f(x) = x2 – 3x + 2f(x) = (x-2)f(x) = |X|

Answer 1

The condition for a function to be even is:

$f(x)=f(-x)$

We substitute x by -x in our options and see of we get the same original function, if we do then it is an even function.

First function:

$f(x)=x^4-x^2$

And for f(-x) here we have:

$f(-x)=(-x)^4-(-x)^2$

Even exponents always give positive results, so:

$f(-x)=x^4-x^2$

This is an even function.