Question

Two functions f and g are defined by 𝑓: 𝑥 →
𝑥
1+𝑥
𝑎𝑛𝑑 𝑔: 𝑥 → 𝑥 − 1, find the composite
function 𝑔𝑜𝑓(𝑥)
A. 𝑥
B.
1
1+
𝑥
C. −𝑥
− 1
𝑥
D. 1 +
𝑥
𝑥

Answer 1

To find the composite function g o f, we plug in the definition of f into g:

g o f (x) = g(f(x)) = g(x/(1+x)) = x/(1+x) - 1

Therefore, the answer is option B: 1/(1+x) - 1.