Functions Test ...

If $$f ( x ) = \left( a - x ^ { n } \right) ^ { 1 / n }$$ where $$a > 0$$ and $$n$$ is a positive integer then $$( f o f ) ( x )$$ is 

$$f:R \rightarrow R$$ such that $$f(x)=\ell n(x+\sqrt {x^{2}+1})$$. Another function $$g(x)$$ is defined such that $$gof(x)=x\ \forall\ x \in\ R$$. Then $$g(2)$$ is -

Let $$f:R\rightarrow R$$ is a function satisfying $$f(2-x)=f(2+x)$$ and $$f(20-x)=f(x)\forall x\in R$$
If $$f(0)=5$$ then the minimum possible no. of values of $$x$$ satisfying $$f(x)=5$$ for $$x=[0.,70]$$, is

Let $$f\left( x \right) = {x^2}$$ and $$g\left( x \right) = {2^x}$$. Then the solution of the equation $$fog\left( x \right) = gof\left( x \right)$$ is

All values of a for which f : R $$ \to R$$ defined by f(x)= $${x^3} + a{x^2} + 3x + 100$$ is a one one functions, are

If $$f ( x ) = \sin ^ { - 1 } ( \sin x ) + \cos ^ { - 1 } ( \sin x ) \text { and } \phi ( x ) = f ( f ( f ( x ) ) )$$ then $$\phi ^ { \prime } ( x )$$

if $$f\left( x \right) = 3x + 2$$ , $$g\left( x \right) = {x^2} + 1$$,then the values of $$\left( {f_og} \right)\left( {{x^2} - 1} \right)$$

Let A = {1,2,3,4,5} and B={1,2,3,4,5}. If $$f:A\rightarrow B$$ is an one-one function and $$f(x)=x$$ holds only for one value of  $$x\epsilon \{ 1,2,3,4,5\} ,$$ then the number of such possible function is  

The domain function $$\sqrt{log_{10}(\frac{5x-x^{2}}{4})}$$ is 

$$f(x) = \mid |x|^2 - 2 |x| -3 \mid$$ is non differentiable at $$k$$ points in its domain , the value of $$k$$ is