The values of the composite functions f(g(x)) and g(f(x)) are (x/4) and (4x - 9),respectively.
We are given two functions, f(x) and g(x). The function f(x) is defined as 1/(x - 3). The function g(x) is defined as (4/x) + 3. A function connects an input to an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. We need to find the composition of the functions.
The first composition is f(g(x)). The composite function is solved below.
f(g(x)) = f((4/x) + 3)
f(g(x)) = 1/([(4/x) + 3] - 3)
f(g(x)) = 1/(4/x)
f(g(x)) = x/4
The second composition is g(f(x)). The composite function is solved below.
g(f(x)) = g(1/(x - 3))
g(f(x)) = (4/[1/(x - 3)]) + 3
g(f(x)) = 4(x - 3) + 3
g(f(x)) = 4x - 12 + 3
g(f(x)) = 4x - 9
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