Relations and F...

If $$f(x)=\begin{cases} 2x+3\quad \quad x\le 1 \\ a^{ 2 }x+1\quad x>1 \end{cases}$$, then the values of $$a$$ for which $$f(x)$$ is injective. 

The relation $$R$$ defined in $$A=\left\{ 1,2,3, \right\} $$ by $$a\ R$$ $$b$$ if $$\left| { a }^{ 2 }-{ b }^{ 2 } \right| \le 5$$. Which of the following is false? 

If the function $$f:[1,\infty )\rightarrow [1,\infty )$$ is defined by $$f\left( x \right) ={ 2 }^{ x\left( x-1 \right)  },$$ then $${ f }^{ -1 }\left( x \right) $$ is

If $$g(x)=1+\sqrt { x } $$ and $$f(g(x))=3+2\sqrt { x } +x$$, then $$f(x)=$$

Let $$X=\left\{ 1,2,3,4 \right\} $$ and $$Y=\left\{ 1,2,3,4 \right\} $$. Which of the following is a relation from $$X$$ to $$Y$$.

Let $$f:\left( 4,6 \right) \rightarrow \left( 6,8 \right) $$ be a function defined by $$f(x)=x+2$$ (where $$[.]$$ denote the greatest integer function), then $$f^{ -1 }\left( x \right) $$ is equal to

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 :

Suppose f and g both are linear function with $$\displaystyle f(x)=-2x+1$$  and $$\displaystyle f \left ( g\left ( x \right ) \right )=6x-7$$ then slope of line $$y=g(x)$$ is

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