Domain, Codomain and Range of a Function

Let $f : R\to R$ be defined by $f\left(x\right)=$$\left\{\begin{array}{ll}2x+3,& \text{ when }x<-2\\ x^2-2,& \text{ when }-2\le x\le 3\\ 3x-1,& \text{ when }x>3\end{array}\right.$.

Find$f\left(-3\right)$

Let $f : R\to R$ be defined by $f\left(x\right)$$=\left\{\begin{array}{ll}2x+3,& \text{ when }x<-2\\ x^2-2,& \text{ when }-2\le x\le 3\\ 3x-1,& \text{ when }x>3\end{array}\right.$.

Find $f\left(-1\right)$.

Let $f : R\to R$ be defined by $f\left(x\right)$$=\left\{\begin{array}{ll}2x+3,& \text{ when }x<-2\\ x^2-2,& \text{ when }-2\le x\le 3\\ 3x-1,& \text{ when }x>3\end{array}\right.$.

Find $f\left(4\right)$.

Let $f : R\to R$ be defined by $f\left(x\right)$$=\left\{\begin{array}{ll}2x+3,& \text{ when }x<-2\\ x^2-2,& \text{ when }-2\le x\le 3\\ 3x-1,& \text{ when }x>3\end{array}\right.$. 

Find$f\left(2\right)$.

Check the following relation is a function? Give reasons. In case of a function, find its domain and range.

$g=\left\{(1,1),(1,-1),(4,2),(9,3),(16,4)\right\}$

Check the following relation is a function? Give reasons. In case of a function, find its domain and range.

$h=(a,b),(b,c),(c,b),(d,c)$

Find the domain and range of the real function, defined by $f\left(x\right)=\frac{x^2}{\left(1+x^2\right)}$ Show that f is many - one.

Check the following relation is a function? Give reasons. In case of a function, find its domain and range.  

$f=\left\{(-1,2),(1,8),(2,11),(3,14)\right\}$.

Find the domain and range of the function

$f:R\to R:f\left(x\right)=x^2+1$

Define a function. What do you mean by the domain and range of a function? Give examples.