I think you mean
[tex] f(x) = \dfrac{15x + 50}{x + 5} [/tex]
First, replace f(x) with y.
[tex] y = \dfrac{15x + 50}{x + 5} [/tex]
Now, switch x and y.
[tex] x = \dfrac{15y + 50}{y + 5} [/tex]
Now we solve for y.
[tex] x(y + 5) = 15y + 50 [/tex]
[tex] xy + 5x = 15y + 50 [/tex]
[tex] xy - 15y = -5x + 50 [/tex]
[tex] y(x - 15) = -5x + 50 [/tex]
[tex] y = \dfrac{-5x+ 50}{x - 15} [/tex]
Now we replace y with [tex] f^{-1}(x) [/tex].
[tex] f^{-1}(x) = \dfrac{-5x+ 50}{x - 15} [/tex]
