Functions Test ...

If $$f : A \rightarrow B $$ defined as $$f(x) = x^2+2x+\frac{1}{1+(x+1)^2}$$ is onto function, then set B is equal to

The domain of the function $$f(x)=\sin \left (\dfrac{1}{x} \right )$$ is

If $$g(f(x) ) = |\sin x |$$ and $$f(g(x))=(\sin\sqrt x)^2$$ , then 

The domain of the function $$f(x) = \dfrac{arc \, cot \, X}{\sqrt{X^2 - [X^2]}}$$, where [X] denotes the greatest integer not greater than x, is :

The set onto which the derivative of the function $$f(x)=x(\log x-1)$$ maps the range $$[1,\infty )$$ is

Let $$E=\{1, 2, 3, 4\}$$ and $$F=\{1, 2\}$$ then the number of onto functions from E to F is

Let $$f\left( x \right) ={ x }^{ 2 },g\left( x \right) ={ 2 }^{ x }$$, then solution set of $$fog\left( x \right) =gof\left( x \right) $$ is

If $$D$$ is the domain of the function $${\sec ^{ - 1}}\left( {\log x} \right)$$, then $$D$$ contains 

Let $$f(x+\dfrac{1}{x})=x^2+\dfrac{1}{x^2}(x\neq 0)$$, then $$f(x)=$$

If f(x)=sin log $$\left( {\sqrt {4 - {x^2}} /\left( {1 - x} \right)} \right)$$ then the domain and range f are (respectively)