Question

G(g(x)) g=(x+14)/(x+2)

Answer 1

`\bf g(x)=\cfrac{x+14}{x+2}~\hspace{8em}g(~~g(x)~~)=\cfrac{g(x)+14}{g(x)+2}\\\\\\(~~g(x)~~)=\cfrac{~~(x+14)/(x+2)+14~~}{(x+14)/(x+2)+2}\implies (~~g(x)~~)=\cfrac{~~(x+14~~+14x+28)/(x+2)~~}{(x+14~~+2x+4)/(x+2)}\\\\\\(~~g(x)~~)=\cfrac{~~(15x+42)/(x+2)~~}{(3x+18)/(x+2)}\implies (~~g(x)~~)=\cfrac{15x+42}{\underline{x+2}}\cdot \cfrac{\underline{x+2}}{3x+18}\\\\\\(~~g(x)~~)=\cfrac{15x+42}{3x+18}\implies (~~g(x)~~)=\cfrac{3(5x+14)}{3(x+6)}\implies (~~g(x)~~)=\cfrac{5x+14}{x+6}`