Give an example of a function which is neither one - one nor onto.

Give an example of a function which is onto but not one - one.

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$f\left(2\right)$.

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 $f\left(-1\right)$.

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$f\left(-3\right)$

Show that the function $f: R\to R: f\left(x\right)=1+x^2$ is many - one into.

Show that the function $f:R\to R:f\left(x\right)=x^4$ is many - one and into.

Show that the function $f: R \to R : f\left(x\right) = x^5$  is one - one and onto.