Two functions f and g are defined by 𝑓: 𝑥 →

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.

Answer 2

To find the composite function g∘f(x), we need to substitute the function f(x) into the function g(x).

Given that f(x) = x/(1+x) and g(x) = x - 1, we can substitute f(x) into g(x) as follows:

g∘f(x) = g(f(x))

Replacing f(x) in g(x) gives:

g∘f(x) = g(x/(1+x))

Now, we replace x in g(x) with x/(1+x):

g∘f(x) = x/(1+x) - 1

Therefore, the composite function g∘f(x) is given by:

g∘f(x) = x/(1+x) - 1

Option B.