Functions · Mathematics · IAT (IISER)

Let $[x]$ denote the greatest integer less than or equal to $x$. The number of positive integer solutions of the equation

$$ \left[\frac{x}{19}\right]=\left[\frac{x}{20}\right] $$

are:

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions such that

$$ g \circ f(x)= \begin{cases}x^2, & \text { if } x \geq 0 \\ e^x-1, & \text { if } x<0\end{cases} $$

Then which of the following statements is correct?