Let \( f(x)=x+3, g(x)=4 x^{2}, h(x)=\sqrt{x-7} \) a. \( f(h(11)) \) b. \( g(f(-8)) \) c. \( h(g(2)) \)

To solve the given expressions with the functions \( f(x) = x + 3 \), \( g(x) = 4x^2 \), and \( h(x) = \sqrt{x - 7} \), let's break it down step by step for each part. a. \( f(h(11)) \) First, we need to find \( h(11) \): \[ h(11) = \sqrt{11 - 7} = \sqrt{4} = 2. \] Now we use this result in \( f(x) \): \[ f(h(11)) = f(2) = 2 + 3 = 5. \] So, \( f(h(11)) = 5 \). b. \( g(f(-8)) \) First, we find \( f(-8) \): \[ f(-8) = -8 + 3 = -5. \] Now we apply \( g(x) \): \[ g(f(-8)) = g(-5) = 4(-5)^2 = 4 \times 25 = 100. \] So, \( g(f(-8)) = 100 \). c. \( h(g(2)) \) First, we calculate \( g(2) \): \[ g(2) = 4(2^2) = 4 \times 4 = 16. \] Now we find \( h(16) \): \[ h(16) = \sqrt{16 - 7} = \sqrt{9} = 3. \] So, \( h(g(2)) = 3 \). In conclusion: a. \( f(h(11)) = 5 \) b. \( g(f(-8)) = 100 \) c. \( h(g(2)) = 3 \)