Functions Test ...

If f(g(x))=5x+2 and g(x)=8x then f(x)=

if $f$ is a bijective function such that $f(x)=\dfrac {\lambda x+\mu}{ax+\beta}$ and  if $f^{-1}(x)=f(x)$, then

If $f\left( x \right) = (1 - x)$ , $x \in \left[ { - 3,3} \right]$ , then the domain of $f\left( {f\left( x \right)} \right)$ is

If $f(x)=\frac{x}{\sqrt{1-x^{2}}}$ and g(x) = $f(x)=\frac{x}{\sqrt{1+x^{2}}}$ , then (fog)(x) =

If $f ( x ) = \left( a - x ^ { n } \right) ^ { 1 / n }$ where $a > 0$ and } $n$ is a positive integer then$( f o f ) ( x )$ is

The function $f ( x ) = \sqrt { \log _ { x ^ { 2 } } x }$ is defined for $x$:

if $f\left( x \right) = \log \left( {\dfrac{{1 +x}}{{1 - x}}} \right)$ and $g\left( x \right) = \dfrac{{3x + {x^3}}}{{1 + 3{x^2}}}$ then $\left( {f(g(x)))} \right)$ is equal to

If $f:R \rightarrow R, f(x)=2x-1$ and $g; R \rightarrow R, g(x)=x^{2}+2$, then $(gof)(x)$ equals-

Let $g(x)=1+x-[x]\quad$ and $f(x)=\begin{cases} -1\quad if\quad x<0 \\ 0\quad \quad if\quad x=0 \\ 1\quad \quad if\quad x>0 \end{cases}$ , then $\forall \:x,fog(x)$ equals 

$f:c \to c$ is defined as $f(x) = \dfrac{{ax + b}}{{cx + d}},bd \ne 0$ then $f$ is a constant function when,