Find (a) \( f(g(x)) \), (b) \( g(f(x)) \), and (c) \( f(f(x)) \). \( f(x)=3 x-7, g(x)=\sqrt{x+7} \) a. \( f(g(x))=\square \) b. \( g(f(x))=\square \) c. \( f(f(x))=\square \)

Let's tackle each part step by step! a. To find \( f(g(x)) \): First, we plug \( g(x) \) into \( f(x) \). So we compute: \[ g(x) = \sqrt{x + 7} \] Now substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(\sqrt{x + 7}) = 3(\sqrt{x + 7}) - 7 \] Thus, \[ f(g(x)) = 3\sqrt{x + 7} - 7 \] b. To find \( g(f(x)) \): We plug \( f(x) \) into \( g(x) \). So we compute: \[ f(x) = 3x - 7 \] Now substitute \( f(x) \) into \( g(x) \): \[ g(f(x)) = g(3x - 7) = \sqrt{(3x - 7) + 7} = \sqrt{3x} \] So, \[ g(f(x)) = \sqrt{3x} \] c. To find \( f(f(x)) \): We will compute this by plugging \( f(x) \) into itself: \[ f(f(x)) = f(3x - 7) = 3(3x - 7) - 7 \] Now simplify: \[ f(f(x)) = 9x - 21 - 7 = 9x - 28 \] Thus, \[ f(f(x)) = 9x - 28 \] In summary: a. \( f(g(x)) = 3\sqrt{x + 7} - 7 \) b. \( g(f(x)) = \sqrt{3x} \) c. \( f(f(x)) = 9x - 28 \)