Which statement(s) verify that $f(x)=\frac{4}{x+1}$ and $g(x)=\frac{4-x}{x}$ are inverse?

A) $f(x)+g(x)=\frac{4}{x+1}+\frac{4-x}{x}=0$
B) $\frac{f(x)}{g(x)}=\frac{\frac{4}{x+1}}{\frac{4-x}{x}}=1$
C) $f(g(x)\; )=\frac{4}{\frac{4-x}{x}+1}=x,g(f(x)\; )=\frac{4-\frac{4}{x+1}}{\frac{4}{x+1}}=x$
D) $f(x)+g(x)=\frac{4}{x+1}+\frac{4-x}{x}=1$
E) $f(g(x)\; )=\frac{4}{\frac{4-x}{x}+1}=1;g(f(x)\; )=\frac{\frac{4}{x+1}}{\frac{4}{x+1}}=1$

Choice A cannot be correct because the sum of the functions is not equal to 0. Choice B cannot be correct because the quotient of the functions is not always equal to 1. Choice D cannot be correct because the sum of the functions is not equal to 1. Choice E cannot be correct because while it correctly shows that both compositions of the functions result in 1, it is not necessary to show both of these compositions to verify that the functions are inverses. Only choice C correctly shows that the composition of the functions equals the input value, which is the definition of inverse functions.