Question

PLEASE SOMEONE HELP I TRULY DO NOT UNDERSTAND

Find F^-1(x), the inverse of F(x).

f(x)-9x^3-4
Show your work please because I don’t understand.

Answer 1

Hi there!

`\large\boxed{f^(-1)(x) = \sqrt[3]{(x+4)/(9) } }`

`f(x) = 9x^(3) - 4`

Find the inverse by replacing f(x) with y and swapping the x and y variables:

`x = 9y^(3) - 4`

Isolate y by adding 4 to both sides:

`x + 4 = 9y^(3)`

Divide both sides by 9:

`(x+4)/(9)= y^(3)`

Take the cube root of both sides:

`y = \sqrt[3]{(x+4)/(9) }\\\\f^(-1)(x) = \sqrt[3]{(x+4)/(9) }`