Question #93699

1 Answer
Feb 3, 2017

Answer:

#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.