CAT (QA) PYQs

If $f(x) = \frac{5x + 2}{3x - 5}$ and $g(x) = x^2 - 2x - 1$, then the value of $g(f(f(3)))$ is

If $f(x + 2) = f(x) + f(x + 1)$ for all positive integers $x$, and $f(11) = 91$, $f(15) = 617$, then $f(10)$ equals

For any positive integer $n$, let $f(n)=n(n+1)$ if $n$ is even, and $f(n)=n+3$ if $n$ is odd. If $m$ is a positive integer such that $8 f(m+1)-f(m)=2$, then $m$ equals