How do you know if #f(x) = 5x^6 + 8x^2 – 16# is an even or odd function?

1 Answer
sente
Nov 26, 2015

#f(x)# is even.

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)#

In this case
#f(-x) = 5(-x)^6 + 8(-x)^2 - 16 = 5x^6 + 8x^2 - 16 = f(x)#

So #f(x)# is even.

(In general, this kind of function can be easily identified as even or odd, as if every term in a sum is even, then so is the sum, and if every term in a sum is odd, then so is the sum).

Related questions
See all questions in Introduction to Twelve Basic Functions
Impact of this question
1202 views around the world
You can reuse this answer
Creative Commons License