Functions Test ...

Which of the following functions is/are injective map(s) ?

Let $$f:\ (-1,1)\rightarrow B$$ be a function defined by $$ f(x)={ \tan }^{ -1 }\cfrac { 2x }{ 1-{ x }^{ 2 } } $$, then $$f$$ is both one-one and onto when B is the interval

The domain of the function $$f(x)=\log_3 \log_{1/3}(x^2+10x+25)+\dfrac {1}{[x]+5}$$ where [.] denotes the greatest integer function) is

If $$f:R\rightarrow \left [\dfrac {\pi}{6}, \dfrac {\pi}{2}\right ), f(x)=\sin^{-1}\left (\dfrac {x^2-a}{x^2+1}\right )$$ is a onto function, then set of values of $$a$$ is

Which one of the following functions is not one-one?

Let f: $$X\rightarrow Y$$ be a function defined by $$f(x)=a \sin \left (x+\dfrac {\pi}{4}\right )+b \cos x+c$$. If f is both one-one and onto, then find the sets $$X$$ and $$Y$$

$$f(x)=x^3+3x^2+4x+b \sin x+c \cos x, \forall x\in R$$ is a one-one function, then the value of $$b^2+c^2$$ is

If $$f(x)=2x+|x|, g(x)=\dfrac {1}{3}(2x-|x|)$$ and $$h(x)=f(g(x))$$, then domain of $$\sin^{-1}\underset {\text {n times}}{\underbrace {(h(h(h(h.....h(x).....))))}}$$ is

The function $$f$$ is one to one and the sum of all the intercepts of the graph is $$5$$. The sum of all the intercept of the graph $$\displaystyle y = f^{-1} \left ( x \right )$$ is

Let $$f\left( x \right) =\left\{ \begin{matrix} 1+|x|,\; x<-1 \\ \left[ x \right] ,\; x\ge -1 \end{matrix} \right. $$ where $$[\cdot]$$ denotes the greatest integer function. Then $$\displaystyle f\left \{f(-2.3) \right\}$$ is equal to