CAT (QA) PYQs

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

Suppose for all integers x, there are two function f and g such that $f(x) + f(x-1) - 1 = 0$ and $g(x) = x^2$. If $f(x^2 - x) = 5$, then the value of the sum $f(g(5)) + g(f(5))$ 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