If A=R- {+1} and function f: A →A is defined by $f(x)=\frac{x+1}{x-1}$ then $f^{-1}(x)$ is given by :
Answer & explanation
Correct answer: option 4
The correct answer is option (4) → $\frac{x+1}{x-1}$
$y=\frac{x+1}{x-1}⇒xy-y=x+1$
so $x(y-1)=y+1$
$x=\frac{y+1}{y-1}⇒f^{-1}(x)=\frac{x+1}{x-1}$