Is the function #f(x)=(1/x^3+x)^5# even, odd or neither?

1 Answer
Nov 17, 2015

Answer:

#f(x) = (1/x^3 + x)^5# is odd.

Explanation:

A function #f(x)# is even if and only if #f(-x) = f(x)#.
A function #f(x)# is odd if and only if #f(-x) = -f(x)#.

To check this function then, we will look at #f(-x)#.

#f(-x) = (1/(-x)^3 + (-x))^5 = (-1/x^3 -x)^5#

#=> f(-x) = ((-1)(1/x^3 + x))^5 = (-1)^5(1/x^3+x)^5#

#=> f(-x) = -(1/x^3 + x)^5 = -f(x)#

Thus in this case #f(x)# is odd.