$($a$)$ Let A $=\{$x E $|$x # $1\}$ and define f$($x$)=**,$ for all x A$.$ Show that fis injective from A into R$.$ What is the range of f$?\%(2$ marks$)$

b$)$ Let g$($x$)=$ x$?$ and f$($x$)=$ x $+2$ for all x R$.$ Let h be the composite function h $=$ go f$.$ Test whether h is a bijection. Find h$-\text{'}($G$),$ whereG $=\{$x ER$|0<$ x $4\}.\%92(2$ marks$)$

c$)$ Give one example for each of the following:$($i$)$ a relation on $\{1,2,3,4\}$ which is reflexive and symmetric but not transi$-$tive.$($i$)$ a relation on $\{1,2,3,4\}$ which is symmetric and transitive but not re$-$flexive.$\%$