For \( f(x)=\sqrt{x} \) and \( g(x)=x+4 \), find a. \( (f \circ g)(x) ; \) b. the domain of \( f \circ g \) a. \( (f \circ g)(x)=\square \) \( ( \) Simplify your answer.)

To find \( (f \circ g)(x) \), you substitute \( g(x) \) into \( f(x) \). Starting with \( g(x) = x + 4 \): \[ (f \circ g)(x) = f(g(x)) = f(x + 4) = \sqrt{x + 4} \] So, \[ (f \circ g)(x) = \sqrt{x + 4} \] Next, let’s determine the domain of \( f \circ g \): Since \( f(x) = \sqrt{x} \), the expression inside the square root must be non-negative. Therefore, we set: \[ x + 4 \geq 0 \] \[ x \geq -4 \] Thus, the domain of \( f \circ g \) is \( [-4, \infty) \). In summary: a. \( (f \circ g)(x) = \sqrt{x + 4} \) b. The domain of \( f \circ g \) is \( [-4, \infty) \).