Find \( (f \circ g)(x) \) and \( (g \circ f)(x) \) and the domain of each. \( f(x)=60, g(x)=0.15 \)

To find \( (f \circ g)(x) \) and \( (g \circ f)(x) \), we need to understand what these compositions mean. 1. **Finding \( (f \circ g)(x) \)**: \[ (f \circ g)(x) = f(g(x)) \] Given \( g(x) = 0.15 \), we substitute this into \( f \): \[ f(g(x)) = f(0.15) \] Since \( f(x) = 60 \) for any input \( x \), we have: \[ f(0.15) = 60 \] Therefore, \[ (f \circ g)(x) = 60 \] 2. **Finding \( (g \circ f)(x) \)**: \[ (g \circ f)(x) = g(f(x)) \] Since \( f(x) = 60 \), we substitute this into \( g \): \[ g(f(x)) = g(60) \] Given \( g(x) = 0.15 \) for any input \( x \), we have: \[ g(60) = 0.15 \] Therefore, \[ (g \circ f)(x) = 0.15 \] 3. **Finding the domains**: - The function \( f(x) = 60 \) is defined for all real numbers, so the domain of \( f \) is \( \mathbb{R} \). - The function \( g(x) = 0.15 \) is also defined for all real numbers, so the domain of \( g \) is \( \mathbb{R} \). Since both functions are defined for all real numbers, the domains of the compositions are: - The domain of \( (f \circ g)(x) \) is \( \mathbb{R} \). - The domain of \( (g \circ f)(x) \) is \( \mathbb{R} \). In summary: \[ (f \circ g)(x) = 60, \quad \text{domain: } \mathbb{R} \] \[ (g \circ f)(x) = 0.15, \quad \text{domain: } \mathbb{R} \]