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

If $f$ and $g$ are two increasing functions such that $fog$ is defined,then what kind of function is $fog$?

If $f(x)=-|x|$,then $(f \circ f \circ f)(x) + (f \circ f \circ f)(-x) =$

Consider $f: N \rightarrow N$,$g: N \rightarrow N$,and $h: N \rightarrow R$ defined as $f(x) = 2x$,$g(y) = 3y + 4$,and $h(z) = \sin z$,$\forall x, y, z \in N$. Show that $h \circ (g \circ f) = (h \circ g) \circ f$.

Give examples of two functions $f: N \rightarrow Z$ and $g: Z \rightarrow Z$ such that $g \circ f$ is injective but $g$ is not injective. (Hint: Consider $f(x) = x$ and $g(x) = |x|$)

Let $f: \{2, 3, 4, 5\} \rightarrow \{3, 4, 5, 9\}$ and $g: \{3, 4, 5, 9\} \rightarrow \{7, 11, 15\}$ be functions defined as $f(2)=3, f(3)=4, f(4)=f(5)=5$ and $g(3)=g(4)=7$ and $g(5)=g(9)=11$. Find $g \circ f$.