If $f(x) = x^2$ and $g(x) = [x^2]$ where $[\cdot]$ represents the greatest integer function then, $(f \circ g)\left(\dfrac{3}{2}\right) + (g \circ f)\left(\dfrac{3}{2}\right)$ is equal to ...

The domain of the function $f(x) = \sqrt{\dfrac{x}{1+x}}$ is $\ldots$

Let $f(x) = ax + b$ and $g(x) = cx + d$. The condition $f(g(x)) = g(f(x))$ holds for all $x$ if and only if ...

If $f(x) = \dfrac{1 - x}{1 + x}$, then $f(f(\cos x)) =$