The value of $a\:\:and\:\:b$ for which $f:R\rightarrow R$ is defined as $f(x)=ax+b$ where $a,b\in R $ is bijection with $fof$ as its identity is ?

Question

$\begin{array}{1 1} a=1\;and\;b \in R \\ a=1,b=0\;or\;a=-1 ,b \in R \\ a= \pm 1,b \in R \\ a= \pm 1, b=0 \end{array}$