Question

find the inverse of f(x)=3x^2(x-4)^3

Answer 1

\(\large f(x)=3x^2(x-4)^3 ?\)

Answer 2

yes :)

Answer 3

$$
\color{blue}{y}=3\color{red}{x}^2(\color{red}{x}-4)^3\\
\text{doing a switcharoo}\\
\color{red}{x}=3\color{blue}{y}^2(\color{blue}{y}-4)^3\\
\text{solving for "y"}\\
$$

Answer 4

whatever "y" gives you, is your \(f^{-1}(x)\)

Answer 5

yes, i got how to do that , but i got lost after it :/

Answer 6

one sec

Answer 7

ok :)

Answer 8

shoot, I need to dash

lemme paste thus far what I have
so you have a binomial raised at the 3rd power
so you expand it by using "newton binomial theorem"
once expanded, you multiply it by its the \(3y^2\) coefficient and
$$
\color{blue}{y}=3\color{red}{x}^2(\color{red}{x}-4)^3\\
\text{doing a switcharoo}\\
\color{red}{x}=3\color{blue}{y}^2(\color{blue}{y}-4)^3\\
\implies
x=3y^2\pmatrix{y^3-3(y^2)(4)+3(y)(4^2)-4^3}\\
\implies x=3y^5-36y^4+144y^3-192y^2
$$

Answer 9

hmm, i seee, can anything else be done?