Question

How do you find the inverse of `f(x)= (x+5)^3-7`?

Answer 1

`bar(f(x)) = root(3)(x+7)-5`

Explanation:

If `bar(f(x))` is the inverse of `f(x)`
then by definition:
`color(white)("XXX")f(bar(f(x))) = x`

So
`color(white)("XXX")f(bar(f(x))) = (bar(f(x))+5)^3-7=x`

`color(white)("XXXXXXXXXX")bar(f(x))+5 color(white)("XXXX")= root(3)(x+7)_`

`color(white)("XXXXXXXXXX")bar(f(x))color(white)("XXXXXX") = root(3)(x+7)-5`