Functions Test ...

Find number of all such functions $$y = f(x)$$ which are one-one?

The number of real linear functions $$f(x)$$ satisfying $$f\left\{ f(x) \right\} =x+f(x)$$

Let $$f:N\times N\rightarrow N-\left\{ 1 \right\} $$ be defined as $$f(m,n)=m+n$$, then function $$f$$ is ______.

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

$$f:R \to R,f\left( x \right) = \dfrac {{x^2} + 2x + c}{{x^2} + 4x + c}$$ is onto only if

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

Domain of function as $$f\left( x \right) = \dfrac{{^3\sqrt {{x^2} - 5x + 6} }}{{{x^2} - x - 6}}$$ is 

Read the following information and answer the three items that follow :
Let $$f(x) = x^2 + 2x - 5 $$ and $$g(x) = 5x + 30$$
Consider the following statements:
1. $$f[g(x)]$$ is a polynomial of degree 3.
2. $$g[g(x)]$$ is a polynomial of degree 2.
Which of the above statements is/are correct ?

Let $$f(x)=\cfrac { 1 }{ 1-x } $$. Then $$\left\{ f\circ \left( f\circ f \right)  \right\} (x)$$

Read the following information and answer the three items that follow :
Let $$f(x) = x^2 + 2x - 5 $$ and $$g(x) = 5x + 30$$
What are the roots of the equation $$g[f(x)] = 0$$ ?