If $f(x) = \frac{x}{x+1}$ and $g(x) = 2x-1$, find $(g\circ f) (x)$.

Question

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?

Don't trust answer keys in books. They're usually wrong. – user85798 Jun 29 '14 at 18:11 — user85798, Jun 29 '14 at 18:11
Thanks really appreciate the feedback. – Cetshwayo Jun 29 '14 at 18:23 — Cetshwayo, Jun 29 '14 at 18:23
Yep, looks like the book forgot the $-1$. – Thomas Andrews Jun 29 '14 at 18:26 — Thomas Andrews, Jun 29 '14 at 18:26

score 4 · Answer 1 · answered Jun 29 '14 at 18:07

4

Wolframalpha and me agree with you, if $$f(x)=\frac{x}{x+1}, g(x)=2x-1 $$ then $$g \circ f(x)=g(f(x))= 2f(x)-1 = \frac{2x}{x+1}-1= \frac{2x-x-1}{x+1}= \frac{x-1}{x+1}.$$

answered Jun 29 '14 at 18:07

Surb

55,662

If $f(x) = \frac{x}{x+1}$ and $g(x) = 2x-1$, find $(g\circ f) (x)$.

1 Answers1