Functions Test ...

$$f:A\rightarrow B$$ will be an into function if

If f (x) = cosx and g (x) = x$$^2$$ then (gof) (x) is ....

Suppose that $$g(x)=1+\sqrt { x } and\quad f(g(x))=3+2\sqrt { x } +x\quad then\quad f(x)\quad is$$

Which one of the following is one-one?

Let $$f:R\rightarrow R$$  defined by $$f\left( x \right) =\frac { { e }^{ { x }^{ 2 } }-{ e }^{ -x^{ 2 } } }{ { e }^{ x^{ 2 } }+{ e }^{ { -x }^{ 2 } } } ,$$ then

The domain of derivative of the function $$f\left( x \right) = \left| {{{\sin }^{ - 1}}\left( {2{x^2} - 1} \right)} \right|$$ is:

Let $$f:R\rightarrow R$$, be defined as $$f(x)={ e }^{ x^{ 2 } }+cosx$$ then f is

If the mapping $$  f(x)=a x+b, a<0  $$ maps $$ [-1,1]  $$ onto $$ [0,2],  $$ then for all values of $$  \theta, A=\cos ^{2} \theta+\sin ^{4} \theta  $$ is such that

l qt f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g be the function satisfying f(x)+g(x)=$$X^{2}$$, the value of the integral $$\int _{ 0 }^{ 1 }{ f(x)g(x)\quad dx\quad is } $$

$$f : R \rightarrow R$$  defined by  $$f ( x ) = \dfrac { x } { x ^ { 2 } + 1 } , \forall x \in R$$  is