CAT (QA) PYQs

Let $f$ be a function such that $f(mn) = f(m)f(n)$ for every positive integers m and n. If $f(1)$, $f(2)$ and $f(3)$ are positive integers, $f(1) < f(2)$, and $f(24) = 54$, then $f(18)$ equals

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

For any non-zero real number x, let $f(x) + 2 f(\frac{1}{x}) = 3x$. Then, the sum of all possible values of $x$ for which $f(x) = 3$, is