For \( f(x)=\sqrt{x} \) and \( g(x)=x+6 \), find the following functions. a. \( (f \circ g)(x) ; b .(g \circ f)(x) \); c. \( (f \circ g)(3) \); d. \( (g \circ f)(3) \) a. \( (f \circ g)(x)=\square \) (Simplify your answer.) b. \( (g \circ f)(x)=\square \) \( ( \) Simplify your answer. \( ) \) c. \( (f \circ g)(3)=\square \) (Simplify your answer.) d. \( (g \circ f)(3)=\square \) (Simplify your answer.)

Let's evaluate each part step by step using the given functions \( f(x) = \sqrt{x} \) and \( g(x) = x + 6 \). ### a. \( (f \circ g)(x) \) \[ (f \circ g)(x) = f(g(x)) = f(x + 6) = \sqrt{x + 6} \] **Answer:** \( (f \circ g)(x) = \sqrt{x + 6} \) ### b. \( (g \circ f)(x) \) \[ (g \circ f)(x) = g(f(x)) = g(\sqrt{x}) = \sqrt{x} + 6 \] **Answer:** \( (g \circ f)(x) = \sqrt{x} + 6 \) ### c. \( (f \circ g)(3) \) \[ (f \circ g)(3) = \sqrt{3 + 6} = \sqrt{9} = 3 \] **Answer:** \( (f \circ g)(3) = 3 \) ### d. \( (g \circ f)(3) \) \[ (g \circ f)(3) = \sqrt{3} + 6 \approx 1.732 + 6 = 7.732 \] **Answer:** \( (g \circ f)(3) = \sqrt{3} + 6 \) (approximately 7.732)