Question

What is the inverse of the function f(x)= 15x+50/x+5

Answer 1

I think you mean

`f(x) = (15x + 50)/(x + 5)`

First, replace f(x) with y.

`y = (15x + 50)/(x + 5)`

Now, switch x and y.

`x = (15y + 50)/(y + 5)`

Now we solve for y.

`x(y + 5) = 15y + 50`

`xy + 5x = 15y + 50`

`xy - 15y = -5x + 50`

`y(x - 15) = -5x + 50`

`y = (-5x+ 50)/(x - 15)`

Now we replace y with
`f^(-1)(x)`.

`f^(-1)(x) = (-5x+ 50)/(x - 15)`