List of top Mathematics Questions on composite of functions asked in MET

If \( f \circ g = |\sin x| \) and \( g \circ f = \sin^2 \sqrt{x} \), then \( f(x) \) and \( g(x) \) are

Let \( f : \mathbb{R} \to \mathbb{R} \) be defined by \( f(x) = \frac{x}{\sqrt{1+x^2}} \), then \( (f \circ f)(x) \) is

The area of the region \([(x,y): x^2 + y^2 \leq 1 \leq x + y]\) is

If \( f(x) = |\cos x| \) and \( g(x) = [x] \), then \( g \circ f(x) \) is equal to