Mathematics - Functions Question with Solution | TestHub

Taking $x=y=1$, we get:

$$f(1)f(1)-f(1)=2$$

$$f^2(1)-f(1)-2=0$$

$$(f(1)-2)(f(1)+1)=0$$

$$f(1)=2(asf(1)>0)$$

Taking $y=1$, we get:

$$f(x)\cdot f(1)-f(x)=x+1$$

$$f(x)=x+1$$

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

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

Thus, (C) is the correct answer.