Solution:

$\begin{aligned} \\ &\text { Here, } F \circ F=I \quad \text { (Given) } \\\\ &\quad F[F(x)]=I(x)=x \\\\ &\text { ie. } \quad F(p x+q)=x \\\\ &\Rightarrow \quad p(p x+q)+q=x \\\\ &\Rightarrow \quad p^2 x+p q+q=x \\\\ &\Rightarrow \quad p^2 x+p q+q-x=0 \\\\ &\Rightarrow \quad\left(p^2-1\right) x+q(p+1)=0\\ \end{aligned}\\ $ …