Relations and F...

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

Let $$f:N\rightarrow Y$$ be a function defined as $$f(x)=4x+3$$, where $$Y=\{y\in N:y=4x+3,$$ for some $$x\in N\}$$. Show that $$f$$ is invertible and its inverse is 

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:

Let $$f : A \rightarrow B$$ be a function defined as $$f(x) = \dfrac {x - 1}{x - 2}$$, where $$A = R - \left \{2\right \}$$ and $$B = R - \left \{1\right \}$$. Then $$f$$ is :

If $$f(x) =x+\tan x$$ and $$f$$ is inverse of $$g$$, then $$g'(x)$$ is equal to

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

$$f:R\rightarrow R$$ is a function defined by $$f(x)=10x-7$$.  If  $$g=f^{-1}$$  then  $$g(x)=$$  

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

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

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