Example 1

If f : x → x + 5 and g : x → x² +2x + 3, find

1. the value of gf (2),
2. the value of fg (2 ),
3. the composite functions fg,
4. the composite functions gf,
5. the composite functions g² ,
6. the composite functions f².

correction for part (c)

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