g(f(x)) = x
What is inverse function?
An inverse function is defined as a function, which can reverse into another function.
[tex]f(x)= \frac{(x + 5)}{(2x + 1)}[/tex]
[tex]g(x)= \frac{(5 - x)}{(2x - 1)}[/tex]
[tex]g(f(x))=g( \frac{(x+5)}{(2x +1)})[/tex]
Substitute the value of f(x),
[tex]g(f(x))= \frac{(5 - \frac{(x + 5)}{(2x + 1)})}{(2 \frac{(x + 5)}{(2x + 1)} - 1)}[/tex]
[tex]g(f(x))= \frac{\frac{10x+5-x-5}{2x+1} }{ \frac{2x+10-2x-1}{2x+1}}[/tex]
[tex]g(f(x)) = \frac{9x}{9}[/tex]
g(f(x)) = x
Hence, g(f(x)) = x
Learn more about inverse function
https://brainly.com/question/2541698
#SPJ2
