if f(x) =-8x+6/5x-1, find f^-1(x)

Question

i'm not sure how to do inverse function questions 

Answer 1

f(x) = (-8x+6) / (5x-1)

 

Let y = f(x):  y = (-8x+6) / (5x-1)

 

Switch x and y:  x = (-8y+6) / (5y-1)

 

Solve for y:  x(5y-1) = -8y+6

 

                  5xy - x = -8y = 6

 

                  5xy + 8y = x + 6

 

                     y(5x+8) = x+6

 

                              y = (x+6) / (5x+8) = f^-1(x)