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) = 2x + 16\\)
(simplify your answer.)

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

Explanation:

Find the formula for (f o g)(x)

Using the Function Composition knowledge point

$$ (f \circ g)(x) = f(g(x)) = f(x+8) = 2(x+8) = 2x + 16 $$

Find the formula for (g o f)(x)

Using the Function Composition knowledge point

$$ (g \circ f)(x) = g(f(x)) = g(2x) = 2x + 8 $$

Evaluate (f o g)(2)

Using the Function Composition knowledge point

$$ (f \circ g)(2) = 2(2) + 16 = 4 + 16 = 20 $$

Evaluate (g o f)(2)

Using the Function Composition knowledge point

$$ (g \circ f)(2) = 2(2) + 8 = 4 + 8 = 12 $$

Answer:

For \(f(x) = 2x\) and \(g(x) = x + 8\), find the following functions.
a. \((f \circ g)(x) =\) <blank>\(2x + 16\)</blank>
b. \((g \circ f)(x) =\) <blank>\(2x + 8\)</blank>
c. \((f \circ g)(2) =\) <blank>\(20\)</blank>
d. \((g \circ f)(2) =\) <blank>\(12\)</blank>