Functions Test ...

The domain of the function $$\displaystyle f(x)=\log_{10}\log_{10}(1+x^{3})$$ is 

Which of the following function is one-one?

The domain of function satisfying $$f(x)+f(x^{-1})=\displaystyle \frac{x^{3}+1}{x}$$, is

The domain of $$f(x)=\sqrt{x-2-2\sqrt{x-3}}-\sqrt{x-2+2\sqrt{x-3}}$$, is

The domain of $$\displaystyle f(x)=\sqrt { \log_{ x^{ 2 }-1 }(x) } $$ is

Let $$\displaystyle f:R\rightarrow A=\left \{ y: 0\leq y< \dfrac{\pi}{2} \right \}$$ be a function such that $$\displaystyle f(x)=\tan^{-1}(x^{2}+x+k),$$ where $$k$$ is a constant. The value of $$k$$ for which $$f$$ is an onto function is 

The domain of the function $$\displaystyle f(x)=\sqrt{\sec^{-1}\left \{ \frac{1-|x|}{2} \right \}}$$ is

The domain of $$\displaystyle f(x)=\sin^{-1} \left ( \frac{1+x^{2}}{2x} \right )+\sqrt{1-x^{2}}$$ is

Let $$\displaystyle f:\left \{ x,y,z \right \}\rightarrow \left \{ a,b,c \right \}$$ be a one-one function and only one of the conditions $$(i)f(x)\neq b, (ii)f(y)=b,(iii)f(z)\neq a$$ is true then the function $$f$$  is given by the set 

If the real-valued function $$\displaystyle f(x)=px+\sin\:x$$ is a bijective function then the set of possible values of $$p\:\in\:R$$ is