Question

What is the inverse function of f(x) = x+1/x

Answer 1

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

Hope this helps!!

Answer 2

Answer:  The required inverse function is given by

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

Step-by-step explanation:  We are given to find the inverse function of the following function :

$f(x)=\dfrac{x+1}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

f(x) = y, which gives that

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

From equation (i), we have

$f(x)=\dfrac{x+1}{x}\\\\\\\Rightarrow y=\dfrac{f^{-1}(y)+1}{f^{-1}(y)}\\\\\\\Rightarrow yf^{-1}(y)=f^{-1}(y)+1\\\\\Rightarrow yf^{-1}(y)-f^{-1}(y)=1\\\\\Rightarrow (y-1)f^{-1}(y)=1\\\\\Rightarrow f^{-1}(y)=\dfrac{1}{y-1}.$

Thus, the required inverse function is given by

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