How do you determine whether f(x)=(2x5)(2x3) 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)=2x52x3.

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

f(x)=2(x)52(x)3

(x)5=x
(x)3=x

hence, f(x)=2x5(2x3), or 2x5+2x3.

this is the negative of f(x), which is +2x52x3.

for the function f(x)=2x52x3, f(x)=f(x).

therefore, f(x)=2x52x3 is an odd function.