Question

let ( f(x) = x + 3 ), ( g(x) = 4x^2 ), and ( h(x) = sqrt{x - 7} ). find the indicated value. ( h(g(2)) )

Explanation:

Step1: Find g(2)

First, we need to find the value of \( g(2) \). The function \( g(x) = 4x^2 \). Substitute \( x = 2 \) into \( g(x) \):
\( g(2) = 4\times(2)^2 = 4\times4 = 16 \)

Step2: Find h(g(2))

Now, we need to find \( h(g(2)) \), which is \( h(16) \) since \( g(2) = 16 \). The function \( h(x) = \sqrt{x - 7} \). Substitute \( x = 16 \) into \( h(x) \):
\( h(16) = \sqrt{16 - 7} = \sqrt{9} = 3 \)

Answer:

3