__Example 1__

If $f:x\mapsto x+5$ , and $g:x\mapsto {x}^{2}+2x+3$ , find

(a) the value of gf(2),

(b) the value of fg(2)

(c) the composite functions fg

(d) the composite functions gf

(e) the composite functions ${g}^{2}$

(f) the composite functions ${f}^{2}$

correction for part (c)

$$\begin{array}{l}fg\left(x\right)=f\left({x}^{2}+2x+3\right)\\ \text{}=\left({x}^{2}+2x+3\right)+5\\ \text{}={x}^{2}+2x+3+5\\ \text{}={x}^{2}+2x+8\end{array}$$

hiii sorry i dont understand where the 5 came for question C for composite functions

Thanks for pointing out our mistake, correction had been made accordingly.