Question

I have to determine if this function is either odd or even or neither.

f(x)=x^3*abs(x^3) + x^3

I do not know how to approach this question as the absolute value is giving me trouble. Please help. Thanks.

Answer 1

A function is even if f(-a) = f(a)
a function is odd if f(-a) = -f(a)

f(a) = a^3(a^3) + a^3 = a^3(a^3 + 1)
f(-a) = -(a^3)(a^3) - a^3
= - (a^3)(a^3 + 1)

notice that abs(a^3) is always positive

So what do you think?

You might try it with numbers, e.g.

f(2) = 8(8) + 8 = 72
f(-2) = -8(8) - 8 = -72 = - f(2)