Question

for \\(f(x) = 2x\\) and \\(g(x) = x + 8\\), find the following functions.
a. \\((f \circ g)(x)\\), b. \\((g \circ f)(x)\\), c. \\((f \circ g)(2)\\), d. \\((g \circ f)(2)\\)

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

$$ g(x) = x + 8 \implies f(g(x)) = f(x + 8) $$

Evaluate the outer function

$$ f(x) = 2x \implies f(x + 8) = 2(x + 8) = 2x + 16 $$

Answer:

For \(f(x) = 2x\) and \(g(x) = x + 8\), find the following functions.

a. \((f \circ g)(x) =\) <blank>\(2x + 16\)</blank>
(Simplify your answer.)