The composite function is obtained by plugging the expression for g(x) into f(x).
To find the composite function, substitute g(x) into f(x):
f(g(x)) = f(x+3)
Now, let's plug this expression into f(x) and simplify:
f(g(x)) = f(x+3) = 1/((x+3)^(2))
So, the composite function that expresses the given correspondence correctly is 1/((x+3)^(2)).
This composite function represents a function that takes an input value, adds 3 to it, squares the sum, and then takes the reciprocal of the squared value.
For example, if we evaluate this composite function at x = 2:
f(g(2)) = 1/((2+3)^(2)) = 1/25
Therefore, the composite function is 1/((x+3)^(2)).
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