Find \( (f \circ g)(x) \) and \( (g \circ f)(x) \) and the domain of each. \( f(x)=48, g(x)=0.12 \) \( (f \circ g)(x)=\square \) (Simplify your answer.)

To find \( (f \circ g)(x) \) and \( (g \circ f)(x) \), we need to understand what these compositions mean. 1. **Composition of Functions**: - \( (f \circ g)(x) \) means we first apply \( g \) to \( x \), and then apply \( f \) to the result of \( g(x) \). - \( (g \circ f)(x) \) means we first apply \( f \) to \( x \), and then apply \( g \) to the result of \( f(x) \). 2. **Given Functions**: - \( f(x) = 48 \) (a constant function) - \( g(x) = 0.12 \) (also a constant function) ### Step 1: Calculate \( (f \circ g)(x) \) First, we find \( g(x) \): \[ g(x) = 0.12 \] Now, we apply \( f \) to \( g(x) \): \[ f(g(x)) = f(0.12) = 48 \] Thus, \[ (f \circ g)(x) = 48 \] ### Step 2: Calculate \( (g \circ f)(x) \) Next, we find \( f(x) \): \[ f(x) = 48 \] Now, we apply \( g \) to \( f(x) \): \[ g(f(x)) = g(48) = 0.12 \] Thus, \[ (g \circ f)(x) = 0.12 \] ### Step 3: Determine the Domains - The domain of \( (f \circ g)(x) \) is the set of all \( x \) for which \( g(x) \) is defined. Since \( g(x) \) is a constant function, it is defined for all real numbers. Therefore, the domain of \( (f \circ g)(x) \) is: \[ \text{Domain of } (f \circ g)(x) = \mathbb{R} \] - Similarly, the domain of \( (g \circ f)(x) \) is the set of all \( x \) for which \( f(x) \) is defined. Since \( f(x) \) is also a constant function, it is defined for all real numbers. Therefore, the domain of \( (g \circ f)(x) \) is: \[ \text{Domain of } (g \circ f)(x) = \mathbb{R} \] ### Final Answers - \( (f \circ g)(x) = 48 \) - \( (g \circ f)(x) = 0.12 \) - Domain of \( (f \circ g)(x) = \mathbb{R} \) - Domain of \( (g \circ f)(x) = \mathbb{R} \)