Functions Test ...

The function $$\displaystyle f(x)=\sqrt{e^{  \cos^{-1}(\log_{4}x^{2})}}$$ is real valued. It is defined if 

The domain of function $$\displaystyle y=\log_{3}(5+4x-x^{2})$$ is 

The domain of the function $$\displaystyle f(x)=\sin^{-1}(x+[x]),$$ where $$[\cdot]$$ denotes the greatest integer function is 

The domain of the function $$\displaystyle f(x)=\log_{e}(x-[x]),$$ where $$[x]$$ denotes the greatest integer function, is 

Let $$\displaystyle f(x)=\log_{x^{2}}25$$ and $$g(x)=\log_{x}5$$, then $$f(x)=g(x)$$ holds for $$x$$ belonging to 

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

The composite mapping $$fog$$ of the map $$f: R\rightarrow R,f(x)=\sin x$$ and $$g: R\rightarrow R, g(x)=x^2$$ is

If $$\displaystyle \left [ x+\left [ x \right ] \right ]\leq 2$$ where $$\displaystyle \left [ x \right ]$$ denotes the greatest integer $$\displaystyle \leq x,$$ then $$x$$ lies in the interval,

Let $$ f:R \rightarrow R$$ and $$g:R \rightarrow R$$ be defined by $$f(x)=x^2+2x-3,g(x)=3x-4$$ then $$(gof) (x)=$$

If $$f(x)=ax+b$$ and $$g(x)=cx+d$$, then $$f(g(x))=g(f(x))$$ implies