Suppose that $g(x) = 1 + \sqrt{x}$ and $f(g(x)) = 3 + 2\sqrt{x} + x$,then $f(x)$ is

If $f(x) = \begin{cases} \sin x, & x \neq n\pi, n \in I \\ 2, & \text{otherwise} \end{cases}$ and $g(x) = \begin{cases} x^2 + 1, & x \neq 0, 2 \\ 2, & x = 0 \\ 4, & x = 2 \end{cases}$,then find $\lim_{x \rightarrow 0} g(f(x))$.

If $f(x) = \begin{cases} \sin x, & x \neq n\pi, n \in \mathbb{Z} \\ 0, & \text{otherwise} \end{cases}$ and $g(x) = \begin{cases} x^2 + 1, & x \neq 0, 2 \\ 4, & x = 0 \\ 5, & x = 2 \end{cases}$,then $\lim_{x \to 0} g(f(x)) = $

If $f : R \rightarrow R$ is defined by $f(x) = x^{2} - 3x + 2$,find $f(f(x))$.

Let $f(x) = 1 - x$, $g(x) = \frac{1}{1 - x}$, and $h(x) = \frac{1}{x}$ be three functions, for $x \neq 0, 1$. If a function $F(x)$ satisfies $f(F(h(x))) = g(x)$, then which of the following is true?

If $f(x) = x^2 - 1$ and $g(x) = 3x + 1$,then $(gof)(x) = $