If function $f: R \rightarrow R$ is defined by $f(x) = (3 - x^5)^{\frac{1}{5}}$,then $(f \circ f)(x) = $ . . . . . . .

Let $f(x) = \begin{cases} x, & x < 0 \\ 1 + x^2, & x \geq 0 \end{cases}$ and $g(x) = 1 + x - [x]$,then the range of $f(g(x))$ is (where $[.]$ denotes the greatest integer function).

If $g(x)=x^{2}+x-1$ and $(g \circ f)(x)=4 x^{2}-10 x+5,$ then $f\left(\frac{5}{4}\right)$ is equal to

Give examples of two functions $f: N \rightarrow N$ and $g: N \rightarrow N$ such that $g \circ f$ is onto but $f$ is not onto.

Let $R$ be a relation '$ < $' from $A$ to $B$,where $A = \{1, 2, 3, 4\}$ and $B = \{1, 3, 5\}$ such that $(a, b) \in R \iff a < b$. Then $R \circ R^{-1}$ is:

If $f$ and $g$ are increasing and decreasing functions respectively from $[0, \infty)$ to $[0, \infty)$,and $h(x) = f(g(x))$ with $h(0) = 0$,then $h(x) - h(1)$ is: