Question

If f(x)= x/x-1 what is f^-1(x)

Answer 1

Answer:

$f^{-1}(x)=\frac{x}{x-1}$

Step-by-step explanation:

our function is  

$f(x)=\frac{x}{x-1}$

we are asked to determine the inverse of the above function . In order to do so we put f(x) = y and separate x in terms of y and in the final answer , we replace x with y and x with h(x)

let us see how do we do that

$y=\frac{x}{x-1}$

multiplying both sides by (x-1)

$y(x-1)=x$

$xy-y=x$

subtracting x from both sides and adding y on both sides

$xy-x=y$

$x(y-1)=y$

dividing both sides by (y-1)

$x=\frac{y}{y-1}$

we now replace x with y and x with $f^{-1}(x)$

$f^{-1}(x)=\frac{x}{x-1}$