Question #93699

1 Answer
sente
Feb 3, 2017

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.

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