Functions Test ...

Let $$N$$ be the set of natural numbers and two functions $$f$$ and $$g$$ be defined as $$f,g : N\to N$$ such that :
$$f (n)= \begin{cases}\dfrac{n+1}{2}& \text{if n is odd}\\ \dfrac{n}{2} & \text{in n is even} \end{cases}$$
and $$g(n) = n - (-1)^n$$. The fog is:

If $$g(x)=x^2+x-1$$ and 
$$(gof)(x)=4x^2-10x+5$$, then
$$f\left(\dfrac{5}{4}\right)$$ is equal to:

 Domain of definition of the function $$\displaystyle{ f }({ x })=\sqrt { \sin ^{ -1 } (2{ x })+\frac { \pi  }{ 6 }  } $$ for real valued $$x$$, is

A constant function $$f:A\rightarrow B$$ will be one-one if

A constant function $$f:A\rightarrow B $$ will be onto if

If $$f:\mathbb{N} \rightarrow \mathbb{N}$$ and $$f(x) = x^{2}$$ then the function is

$$f(x)=1$$, if $$x$$ is rational and $$f(x)=0$$, if $$x$$ is irrational
then  $$(fof)  (\sqrt{5})=$$

The domain of $$f(x) = x!$$  is

If $$f(x) = 3x + 2, g(x) = x^2 + 1$$, then the value of $$(fog) (x^2 +1)$$ is

If $$f:A\rightarrow B $$ is surjective then