$\text{ If the function }f\left(x\right)=\left\{\begin{array}{l}x+1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{ if }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}x\le 1\\ 2x+1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{ if }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1<x\le 2\end{array}\right.\text{ and }g\left(x\right)=\left\{\begin{array}{l}{x}^2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-1\le x\le 2\\ x+2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\le x\le 3\end{array}\right.\text{ then the number of roots of }$$\text{ the equation }f\left(g\right(x\left)\right)=2\text{ is }$

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