CAT (QA) PYQs

If $f(ab) = f(a)f(b)$ for all positive integers $a$ and $b$, then the largest possible value of $f(1)$ is

For all real values of x, the range of the function f(x) = $\frac{x^2+2x+4}{2x^2+4x+9}$ is

Let $f(x) = x^2$ and $g(x) = 2^x$, for all real $x$. Then the value of $f(f(g(x)) + g(f(x)))$ at $x = 1$ is