Question

A function $f:R\to R$ satisfy the equation $f\left(x\right)f\left(y\right)-f\left(xy\right)=x+y$ for all $x,y\in R$ and $f\left(y\right)>0$, then ?

Answer 1

Let $x,y=1$

$\Rightarrow y^2-y-2=0$ $\left(f\right(1)=y)$

$\Rightarrow y^2-2y+y-2$

$\Rightarrow y(y-2)+1(y-2)=0$

$\Rightarrow y=-1$ (y > 0)y=2$

Let $y=1$ now

$f\left(x\right).2-f\left(x\right)=x+1$

$\Rightarrow f\left(x\right)=x+1$.