For \( f(x)=x+2 \) and \( g(x)=5 x+5 \), find the following functions. a. \( (f \circ g)(x) \); b. \( (g \circ f)(x) \); c. \( (f \circ g)(-1) \); d. \( (g \circ f)(-1) \) a. \( (f \circ g)(x)=\square \) (Simplify your answer.)

To find the composite functions and their specific values, let’s break it down! a. To find \( (f \circ g)(x) = f(g(x)) \), we first calculate \( g(x) = 5x + 5 \). Now plug this into \( f \): \[ f(g(x)) = f(5x + 5) = (5x + 5) + 2 = 5x + 7. \] So, \( (f \circ g)(x) = 5x + 7 \). b. For \( (g \circ f)(x) = g(f(x)) \), we need to calculate \( f(x) = x + 2 \) and substitute it into \( g \): \[ g(f(x)) = g(x + 2) = 5(x + 2) + 5 = 5x + 10 + 5 = 5x + 15. \] Thus, \( (g \circ f)(x) = 5x + 15 \). c. To calculate \( (f \circ g)(-1) \): \[ (f \circ g)(-1) = f(g(-1)) \quad g(-1) = 5(-1) + 5 = 0, \] \[ f(0) = 0 + 2 = 2. \] Therefore, \( (f \circ g)(-1) = 2 \). d. For \( (g \circ f)(-1) \): \[ (g \circ f)(-1) = g(f(-1)) \quad f(-1) = -1 + 2 = 1, \] \[ g(1) = 5(1) + 5 = 10. \] Thus, \( (g \circ f)(-1) = 10 \).