<s>[INST] If $f(x) = \frac{x}{x+1}$ and $g(x) = 2x-1$, find $(g\circ f) (x)$. If $f(x) = \frac{x}{x+1}$ and $g(x) = 2x-1$, find $(g\circ f)(x)$. 
My answer is $\frac{x-1}{x+1}$. However, the answer key in the book states $\frac{2x}{x+1}$. How is that? Is the book wrong? 
 [/INST] Wolframalpha and me agree with you, if
$$f(x)=\frac{x}{x+1}, g(x)=2x-1 $$ then
$$g \circ f(x)=g(f(x))= 2f(x)-1 = \frac{2x}{x+1}-1= \frac{2x-x-1}{x+1}= \frac{x-1}{x+1}.$$
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