Question

G(x)=(5-x)/(2x-1) f(x)= (x+5)/(2x+1) what is g(f(x))

Answer 1

`\bf \begin{cases} g(x)=\cfrac{5-x}{2x-1}\\\\ f(x)=\cfrac{x+5}{2x+1} \end{cases}\qquad g(~~f(x)~~)=\cfrac{5-f(x)}{2[f(x)]+1} \\\\\\ g(~~f(x)~~)=\cfrac{5-\left((x+5)/(2x+1) \right)}{2\left((x+5)/(2x+1) \right)-1}\implies g(~~f(x)~~)=\cfrac{(5(2x+1)-(x+5))/(2x+1)}{(2x+10)/(2x+1)-1}`


`\bf g(~~f(x)~~)=\cfrac{(10x+5-x-5)/(2x+1)}{(2x+10-1(2x+1))/(2x+1)}\implies g(~~f(x)~~)=\cfrac{(9x)/(2x+1)}{(2x+10-2x-1)/(2x+1)} \\\\\\ g(~~f(x)~~)=\cfrac{(9x)/(2x+1)}{(9)/(2x+1)}\implies g(~~f(x)~~)=\cfrac{\underline{9} x}{\underline{2x+1}}\cdot \cfrac{\underline{2x+1}}{\underline{9}} \\\\\\ g(~~f(x)~~)=x`