Functions Test ...

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

Let $$f:R\rightarrow R$$ be a function defined by $$f(x)=\left\{ \left|\cos x\right|\right\},$$ where $$\left\{x\right\}$$ represents fractional part of $$x$$. Let $$ S$$ be the set containing all real values $$x$$ lying in the interval $$[0,2\pi]$$ for which $$f(x)\neq \left|\cos x\right|.$$ Then, number of elements in the set $$ S$$ is

If $$f(x)$$ is defined in $$[-3,3]$$ then find the domain of definition of $$f(|2x+3|)$$

The domain of the function $$ f(x)=\cos^{-1}(\sec (\cos^{-1}x))+\sin ^{-1}(\ \text {cosec} (\sin ^{-1}x))$$is

If $$f_{0}(x)\, =\, \dfrac{x}{(x\, +\, 1)}$$ and $$f_{n\, +\, 1}\, =\, f_{0}\circ f_{n}(x)$$ for $$n = 0, 1, 2,\cdots$$ then $$f_{n}(x)$$ is

If the function $$f : R \rightarrow$$ A given  by $$f(x)\, =\, \displaystyle \frac{x^{2}}{x^{2}\, +\, 1}$$ is a surjection, then A is

If $$\displaystyle \log_{1/3} \frac{3x -1}{x + 2}$$ is less than unity then $$x $$ must lie in the interval 

If $$f(x)=\begin{cases} 2x+3\quad \quad x\le 1 \\ a^{ 2 }x+1\quad x>1 \end{cases}$$, then the values of $$a$$ for which $$f(x)$$ is injective. 

The domain of the function $$f\left( x \right)=_{  }^{ 24-x }{ { C }_{ 3x-1 } }+_{  }^{ 40-6x }{ { C }_{ 8x-10 } }$$ is

The domain of $$f(x)\, =\,\sqrt{\displaystyle \frac{1\, -\,|\, x\, |}{2\, -\, |x|}}$$ is