# Thread: by finding inverse of the function, solve the equation

1. ## by finding inverse of the function, solve the equation

I don't get how can we solve an equation by finding the inverse of that function. What has the inverse of that function got to do with solving the equation?

Function is:

f(x) = (x + 3) / (x -5)

Equation is:

(x+3) / (x-5) = 2

2. Originally Posted by struck
I don't get how can we solve an equation by finding the inverse of that function. What has the inverse of that function got to do with solving the equation?

Function is:

f(x) = (x + 3) / (x -5)

Equation is:

(x+3) / (x-5) = 2

So you want to solve f(x) = 2.

Apply the inverse function $f^{-1}$ to both sides:

$f^{-1}(f(x)) = f^{-1}(2)$.

But $f^{-1}(f(x)) = x$.

Therefore $x = f^{-1}(2)$.

So the solution to $\frac{x+3}{x-5} = 2$ is $x = f^{-1}(2)$.

You know how to find the inverse of $f(x) = \frac{x+3}{x-5}$ ? (No? This thread here might give you some clues ......)