Question

Question #93699

Answer 1

`f(x) = xsin(x)` is even.

Explanation:

We can tell if a function `f(x)` is even or odd by examining what happens to `f(-x)`. If `f(-x) = f(x)`, then it is even. If `f(-x) = -f(x)`, then it is odd. It is possible for a function to be both even and odd (in the case where `f(x) = 0`) or neither even nor odd.

For the function in question, noting that `sin(-x) = -sin(x)`, we have

`f(-x) = (-x)sin(-x)`

`=-x(-sin(x))`

`=xsin(x)`

`=f(x)`.

Thus the function is even.