Functions Test ...

The domain of the function $$\phi \left( x \right) = {\log _7}\left( { - {{\log }_{\frac{1}{2}}}\left( {1 + \frac{1}{{\sqrt[4]{x}}}} \right) - 1} \right)$$ is 

If f is even function and g is an odd function, then $$f_og$$ is ............function.

If $$f\left( x \right) =\begin{cases} 2+x,\quad x\ge 0 \\ 2-x,\quad x<0 \end{cases}$$ then $$f\left( f\left( x \right)  \right) $$ is given by

The domain of the function $$y(x)$$ given by $${2^x} + {2^r} = 2$$ for all $$r \in ( - \infty ,1)$$ is:

Let $$f:X \to \left[ {1,\,27} \right]$$ be  a function by $$f\left( x \right) = 5\sin x + 12\cos x + 14$$. The set $$X$$ so that $$f$$ is one-one and onto is 

If : $$f(x) = 5 {x}^{2}$$, $$g(x) = 3x^{4}$$, then : $$(fog) (-1) =$$ 

Let $$g\left( x \right) =1+x-\left[ x \right] $$ and $$f\left( x \right) =\begin{cases} -1,x<0 \\ 0,x=0 \\ 1,x>0 \end{cases}$$ Then for all $$x,f\left( g\left( x \right) \right) $$ is equal to (where $$\left[ . \right] $$ represents the greatest integer function)

The distinct linear functions which maps from $$[-1,1]$$ onto $$[0,2]$$ are 

For $$a,\ b\ \in \ R-\left\{ 0 \right\}$$, let $$f(x)=ax^{2}+bx+a$$ satisfies $$f\left(x+\dfrac{7}{4}\right)=f\left(\dfrac{7}{4}-x\right) \forall \ x\ \in\ R$$.
Also the equation $$f(x)=7x+a$$ has only one real distinct solution. The minimum value of $$f(x)$$ in $$\left[0,\dfrac{3}{2}\right]$$ is equal to

If function $$f\left( x \right) = \frac{1}{2} - \tan \left( {\frac{{\pi x}}{2}} \right);\left( { - 1 < x < 1} \right)$$ and $$g\left( x \right) = \sqrt {3 + 4x - 4{x^2}} $$, then the domain of $$gof$$ is