Question

given \\(f(x) = 2\sqrt{x}\\) and \\(g(x) = 5x\\), evaluate the following expressions.

(a) \\((f \circ g)(4)\\) (b) \\((g \circ f)(2)\\) (c) \\((f \circ f)(1)\\) (d) \\((g \circ g)(0)\\)

part 1 of 4

(a) \\((f \circ g)(4) = \\)

(type an exact answer, using radicals as needed. simplify your answer.)

Explanation:

Define the composite function expression

Using the Composite Functions knowledge point

$$ (f \circ g)(4) = f(g(4)) $$

Evaluate the inner function

Using the Function Evaluation knowledge point

$$ g(4) = 5(4) = 20 $$

Evaluate the outer function

Using the Function Evaluation knowledge point

$$ f(20) = 2\sqrt{20} = 2\sqrt{4 \cdot 5} = 4\sqrt{5} $$

Answer:

Given \(f(x) = 2\sqrt{x}\) and \(g(x) = 5x\), evaluate the following expressions.

(a) \((f \circ g)(4) =\) <blank>\(4\sqrt{5}\)</blank>