Question

Hi, given f(x) = 5x^3 - 2x and g(x) = 3x^3, is g(f(x)) , is the answer 375x^9 - 450x^7 + 180x^5 - 24x^3?

Answer 1

Given,

The expression is,

$\begin{gathered} f(x)=5x^3-2x \\ g(x)=3x^3 \end{gathered}$

Required

The value of g(f(x)).

The value of g(f(x)).

$\begin{gathered} g(f(x))=g(5x^3-2x) \\ =3(5x^3-2x)^3 \\ =3(125x^9-150x^7+60x^5-8x^3) \\ =375x^9-450x^7+180x^5-24x^3 \end{gathered}$

Hence, the value of g(f(x)) is 375x^9 - 450x^7 + 180x^5 - 24x^3.