CAT (QA) PYQs

Let r be a real number and $f(x) = \begin{cases} 2x-r & \text{if } x \ge r \\ 1 & \text{if } x < r \end{cases}$. Then, the equation $f(x) = f(f(x))$ holds for all real values of x where.

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