Find a formula for the inverse of the function: f(x)=2x+y^-1?

Question

is it 3/y??

Answer 1

2x+y^(-1) =z

x=(z-y^(-1))/2

Now switch x with z and you obtain:

f^(-1)(x) = (x-y^(-1))/2

In general you denote f(x) by y but since y is a constant that already appears in the function formula, you have to denote it by z

Answer 2

The easiest way is to switch y and x, and then solve for y. If you switch x and y you'll get x=2y+x^-1. Solve this for y and you'll have your inverse. It should come out to be y=(1/2)x-(1/2)x^-1. To check your work you can graph them in a calculator. If they're reflections of each other over the line y=x, you know you did it right!