What is the Order of operations for finding the inverse of a function AND solving.

Question

I have $y=4(x+2)^3$. So first part of taking the inverse is switching the variables $x$ and $y$ so you'd have $x=4(y+2)^3$. Why does the exponent $3$ get put in front of the square root symbol?

The answer they have here is $y= \sqrt[3]{\dfrac{x}{4}} - 2$

Answer 1

One more chance to state my annoyance that Latex uses "\sqrt[n]{x}" for the nth root: $\sqrt[n]{x}$! This NOT an "exponent 3 in front of a square root", it is the "third root", the inverse of third power: $2^3= 8$ so $\sqrt[3]{8}= 2$.

Answer 2

If I understood your question correctly $$ \sqrt[3]{x/4} - 2 =(x/4)^{1/3} -2 $$

Answer 3

$y = 4(x+2)^2 \Leftrightarrow y = 4x^2 + 16x + 4 $

Solve that as a quadratic trinomial with respect to $x$ and then swap $x->y$.

$4x^2 + 16x + 4 - y = 0$ ....

You get : http://www.wolframalpha.com/input/?i=f(x)+%3D+4x%5E2+%2B+16x+%2B+4+find+inverse