inverse formula

Question

Find a formula for the inverse. 

f(x)=7x+2/5x+9 

f^-1(x)=__. 

help is greatly appreciated!

Answer 1

Let y = (7x+2)/(5x+9)

 

Switch x and y:  x = (7y+2)/(5y+9)

 

Solve for y:  x(5y+9) = 7y+2

 

                 5xy - 7y = 2-9x

 

                    y(5x-7) = 2-9x

 

                          y = (2-9x)/(5x-7)

 

So, f^-1(x) = (2-9x)/(5x-7)