CAT (QA) PYQs

A function $f$ maps the set of natural numbers to whole numbers, such that $f (xy) = f (x) f (y) + f (x) + f (y)$ for all $x, y$ and $f (p) = 1$ for every prime number $p$. Then, the value of $f (160000)$ is

For real values of $x$, the range of the function $f(x)=\frac{2x-3}{2x^2+4x-6}$ is

If $f(x)=x^{2}-7 x$ and $g(x)=x+3$, then the minimum value of $f(g(x))-3 x$ is