Question

What is the inverse of the function f(x)=19/x^3

Answer 1

step 1: replace f(x) with y ⇒ y=
`(19)/( x^(3) )`

step 2: switch the x and y ⇒ x=
`(19)/( y^(3) )`

step 3: solve for y using algebra ⇒
`xy^(3) =19` ⇒
`y^(3)= (19)/(x)` ⇒
`y= \sqrt[3]{ (19)/(x) }`

step 4: switch y to
`f ^(-1)(x)` and this known as "the inverse of f(x)