Question

Question #0dd78

Answer 1

`g(x)` is an even function.

Explanation:

If `g(-x)=g(x)`, the function is even, and if `g(-x)=-g(x)`, it is odd.

To find out which one it is, we plug in `-x`:
`g(-x)=(-x)^2+cos^2(-x)`

Cosine is an even function, and a negative squared is positive, so the minus signs just disappear:
`g(-x)=x^2+cos^2(x)=g(x)`

Since `g(-x)=g(x)`, we can conclude that `g(x)` is an even function.