Question

given: \\(g(x) = \sqrt{x - 4}\\) and \\(h(x) = 2x - 8\\).

what is \\(g(h(10))\\)?

\\(\circ\quad 2\sqrt{2}\\)
\\(\circ\quad \sqrt{6}\\)
\\(\circ\quad \sqrt{6} - 8\\)
\\(\circ\quad 2\sqrt{6} - 8\\)

Explanation:

Evaluate the inner function

$$ h(10) = 2(10) - 8 = 20 - 8 = 12 $$

Evaluate the outer function

$$ g(h(10)) = g(12) = \sqrt{12 - 4} = \sqrt{8} $$

Simplify the radical expression

$$ \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} $$

Answer:

• (A) \(2\sqrt{2}\) (Correct answer)
• (B) \(\sqrt{6}\)
• (C) \(\sqrt{6} - 8\)
• (D) \(2\sqrt{6} - 8\)