Functions Test ...

Which of the following is an onto function

Let f : {x,y,z} $$\rightarrow$$ {a,b,c} be a one-one function. It is known that only one of the following statment is true, and only one such function exists :

The function $$f(x)$$ is defined on the interval $$[0, 1]$$. Find the domain of the function:

If $$f(x)=\begin{cases} x+1,\quad \quad if\quad x\, \leq \, 1 \\ 5-x^{ 2 }\quad \quad if\quad x>1 \end{cases},g(x)=\begin{cases} x\quad \quad if\quad x\leq 1 \\ 2-x\quad if\quad x>1 \end{cases}$$

If $$g(x) = 2x + 1$$ and $$h(x) = 4x^{2} + 4x + 7$$, find a function $$f$$ such that $$f o g = h$$

Which of the following are two distinct linear functions which map the interval $$[-1, 1]$$ onto $$[0, 2]$$

Find domain of the given function:

The functions whose domain is $$R$$ are