Question

for (f(x) = 1 - x) and (g(x) = 4x^2 + x + 3), find the following functions.
a. ((f \circ g)(x)), b. ((g \circ f)(x)), c. ((f \circ g)(3)), d. ((g \circ f)(3))

a. ((f \circ g)(x) = \square
(simplify your answer)

Explanation:

Define the composition of functions

$$ (f \circ g)(x) = f(g(x)) $$

Substitute the inner function

$$ (f \circ g)(x) = f(4x^2 + x + 3) $$

Evaluate and simplify the outer function

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Answer:

For \(f(x) = 1 - x\) and \(g(x) = 4x^2 + x + 3\), find the following functions.

a. \((f \circ g)(x) =\) <blank>\(-4x^2 - x - 2\)</blank>