## anonymous one year ago Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

1. zepdrix

$\large\rm f(\color{orangered}{x})=(\color{orangered}{x})^3+4$Let's replace our x with g(x). We're going to plug the entire g(x) function into f(x).$\large\rm f(\color{orangered}{g(x)})=(\color{orangered}{g(x)})^3+4$On the right side, we'll replace g(x) which what it really is:$\large\rm f(\color{orangered}{g(x)})=(\color{orangered}{\sqrt[3]{x-4}})^3+4$

2. zepdrix

Recall that cube power and cube root are inverse functions, so they "undo" one another.$\large\rm f(\color{orangered}{g(x)})=(x-4)+4$So does f(g(x)) simplify to x?