Functions Test ...

Given $$\displaystyle f\left ( x \right )=\log \left ( \frac{1+x}{1-x} \right )$$ and $$\displaystyle g\left ( x \right )=\frac{3x+x^{3}}{1+3x^{2}}, fog (x)$$ equals

The domain of definition of the function $$\log \cos x$$ is

A function $$R$$ on the set $$N$$ of natural numbers is defined as $$\displaystyle R= \left \{ \left ( 2n,2n+1 \right ):n \epsilon N \right \}$$ The domain of $$R$$ is

If $$\displaystyle y= \sin ^{-1}\frac{x-1}{x+1}+\log \left ( 2-x \right )$$, then its domain is:

If $$\displaystyle A= \left \{ x:-1\leq x\leq 1 \right \}=B.$$ Discuss the following function w.r.t one-one onto bijective and write their characteristics.

If $$\left[ \log _{ 10 }{ x }  \right] =1$$, then $$x$$ lies in which of the following interval

If $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$ are functions defined by $$f(x)=3x-1; g(x)=\sqrt{x+6}$$, then the value of $$(g\circ f^{-1})(2009)$$ is 

If $$\displaystyle y= 2^{-x}+\cos ^{-1}\left ( \frac{x}{2}-1 \right )+\log \sqrt{x-\left [ x \right ]},$$then its domain is given by

Let $$f(x)=x^{2}-2x$$ and $$g(x)=f(f(x)-1)+f(5-f(x)),$$ then

The domain of the function $$f(x)\, =\, \displaystyle \frac{1}{\log_{10}(1\, -\, x)}\, +\, \sqrt{x\, +\, 2}$$, is