Two functions f and g are defined by š: š„ ā
š„
1+š„
ššš š: š„ ā š„ ā 1, find the composite
function ššš(š„)
A. š„
B.
1
1+
š„
C. āš„
ā 1
š„
D. 1 +
š„
š„
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.
To find the composite function gāf(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:
gāf(x) = g(f(x))
Replacing f(x) in g(x) gives:
gāf(x) = g(x/(1+x))
Now, we replace x in g(x) with x/(1+x):
gāf(x) = x/(1+x) - 1
Therefore, the composite function gāf(x) is given by:
gāf(x) = x/(1+x) - 1
Option B.