The composite function f(g(4)) has a value = 182, given f(x) = x² + x, and g(x) = 3x + 1.
What is the combination of functions?
f(g(x)) or (f ∘ g)(x) represents the aggregate of functions f(x) and g(x), wherein g(x) acts first. It is a function that combines more functions to supply some other function. The output of one function inside the parenthesis will become the input of the outer function in composite functions. i.e.,
g(x) is the input of f(x) in f(g(x)).
f(x) is the input of g(x) in g(f(x)).
How can we solve the given question?
We are given functions:
f(x) = x² + x
g(x) = 3x + 1
We are asked to discover the value of the composite function f(g(4)).
We first discover the value of g(4) with the aid of using substituting x = 4 in g(x).
∴ g(4) = 3(4) + 1 = 12 + 1 = 13.
Now, we use the value of g(4) = 13, in f(x) to compute the value of f(g(4)).
∴ f(g(4)) = f(13).
To discover f(13), we substitute x = 13 in f(x)
∴ f(13) = 13² + 13 = 169 + 13 = 182.
∴ The composite function f(g(4)) = 182, given f(x) = x² + x, and g(x) = 3x + 1.
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