How do you determine whether f(x)=(2x^5)-(2x^3) is an odd or even function?

1 Answer
May 22, 2018

see below

Explanation:

the definition of an odd function is the characteristic f(-x) = -f(x).

if you swap a certain x-value for its additive inverse, then the y-value will also change to its additive inverse.

here, f(x) = 2x^5 - 2x^3.

f(-x) would be the new expression when all the xs were swapped for -xs, so:

f(-x) = 2(-x)^5 - 2(-x)^3

(-x)^5 = -x
(-x)^3 = -x

hence, f(-x) = -2x^5 - (-2x^3), or -2x^5 + 2x^3.

this is the negative of f(x), which is +2x^5 - 2x^3.

for the function f(x) = 2x^5 - 2x^3, f(-x) = -f(x).

therefore, f(x) = 2x^5 - 2x^3 is an odd function.