Find the inverse of the function? f^-1(x)=?

Question

Hello I am back and stuck on the last two questions out of 30.  Find the inverse of the function f(x)=18/(x-17)+13.  f^-1(x)=?  Please include steps so I may see where I am messing up. Thanks so much!

Answer 1

If we write y=f(x)=18/(x-17)+13, then the inverse is expressing x in terms of y.

Multiply through by x-17: y(x-17)=18+13(x-17)=18+13x-221.

xy-17y=13x-203, xy-13x=17y-203, x(y-13)=17y-203, x=(17y-203)/(y-13).

f^-1(x)=(17x-203)/(x-13).

CHECK

f(18)=18+13=31, so f^-1(31) should be 18: (17*31-203)/(31-13)=324/18=18, which is expected.