# Algebra

Determine if the function is even, odd or neither.

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

f^-1x=2(-x)^5+2(-x)^3
f^-1x=-2x^5+-2x^3
f^-1x=-2x^5-2x^3
f(x)=2x^5+2x^3
f^-1x=2(-x)^5+2(-x)^3
f^-1x=-2x^5+2(-x)^3
f^-1x=(-2x^5)+(-2x^3)
f^-1x=-2x^5-2x^3
Not even. This function is odd.

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f(-x) = 2(-x)^5 + 2(-x)^3
but (-x)^5 = - x^5
and (-x)^3 = - x^3
so
f(-x) = -2 x^5 - 2 x^3
= -f(x)
so odd because f(-x) = - f(x))

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