If $f(x) = (p - x^n)^{1/n}$, $p > 0$ and $n$ is a positive integer, then $f[f(x)]$ is equal to

If $f: R \rightarrow R$ and $g: R^{+} \rightarrow R$ are such that $g\{f(x)\}=|\sin x|$ and $f\{g(x)\}=(\sin \sqrt{x})^2$, then a possible choice for $f$ and $g$ is

If $f$ is an increasing function and $g$ is a decreasing function, and $fog$ is defined, then what kind of function is $fog$?

Find $g \circ f$ and $f \circ g,$ if $f(x)=|x|$ and $g(x)=|5x-2|.$

If $f: R \to R$ is defined by $f(x) = (x + 1)^2$ and $g: R \to R$ is defined by $g(x) = x^2 + 1$,then $(fog)(-3)$ equals:

If $R$ is a relation from a set $A$ to a set $B$ and $S$ is a relation from $B$ to a set $C$,then the relation $S \circ R$ is: