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).

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