Question

the function f(x)=(x+6)^3 is one to one.
find an equation for f^-1(x), the inverse function

Answer 1

there's two ways to approach this (both equivalent)
1) this function is one that adds 6 to x and then cubes it, so you are looking for something that does the opposite, so it must first cube root x and then subtract 6 from it.
2) let f(x) = y, so y = (x + 6)^3, now switch x and y, and solve for y.
x = (y + 6)^3 -> y + 6 = x^(1/3) -> y = x^(1/3) - 6