Question

If f(x) is an even function and g(x) is an odd function, which of the following must be even?

Answer 1

We are given an even function and a odd function. The composition of any function with an even function is even and the composition of an even function with an odd function is even, therefore, I is even.

The sum of an even and a odd function is not even nor odd, and their product is odd, therefore only I is even.