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Answer :
Final answer:
The function f(g(x)) can be found by substituting g(x) into f(x). This gives f(g(x)) = (3 - x) / ((3 - x) + 5), which simplifies to f(g(x)) = (3 - x) / (8 - x).
Explanation:
To find the function that represents f(g(x)), we must substitute the function g(x) = 3 - x into the function f(x) = x/(x + 5). That means wherever we see an x in f(x), we replace it with (3 - x).
Doing this, we get:
f(g(x)) = (3 - x) / ((3 - x) + 5)
Then, simplify:
f(g(x)) = (3 - x) / (8 - x)
So, the function f(g(x)) is (3 - x) / (8 - x).
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