Question

Find (f • g) where f(x)=1/x+1 and g(x)=-1/x

a. x/x-1
b. -x+1/x
c. 1/x+1
d. x+1/x

Answer 1

The composition (f • g)(x) where f(x) = 1/(x+1) and g(x) = -1/x results in x/(x-1), which is answer choice (a).

Step-by-step explanation:

The student has asked to find the composition of the functions f(x) = 1/(x+1) and g(x) = -1/x. The composition (f • g)(x) is found by substituting g(x) into f(x). So, we calculate f(g(x)):

1. First, find g(x): g(x) = -1/x.
2. Next, substitute g(x) into f(x): f(g(x)) = f(-1/x) = 1/((-1/x) + 1).
3. Simplify the expression: 1/((-1/x) + 1) = 1/((-1+x)/x) = 1 • (x/(-1+x)) = x/(-1+x).
4. Rewrite the result to match the answer choices: x/(x-1).

Therefore, the correct answer is (a) x/(x-1).