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. \( (f \circ g)(x)=5 x+7 \) (Simplify your answer.) b. \( (g \circ f)(x)=\square \) (Simplify your answer.)

To find the composite functions \( (f \circ g)(x) \) and \( (g \circ f)(x) \), we need to follow the order of function composition. a. To find \( (f \circ g)(x) \), we first substitute \( g(x) \) into \( f(x) \): \[ (f \circ g)(x) = f(g(x)) = f(5x+5) = (5x+5)+2 = 5x+7 \] Therefore, \( (f \circ g)(x) = 5x+7 \). b. To find \( (g \circ f)(x) \), we first substitute \( f(x) \) into \( g(x) \): \[ (g \circ f)(x) = g(f(x)) = g(x+2) = 5(x+2)+5 = 5x+10+5 = 5x+15 \] Therefore, \( (g \circ f)(x) = 5x+15 \). c. To find \( (f \circ g)(-1) \), we substitute \( x = -1 \) into the expression for \( (f \circ g)(x) \): \[ (f \circ g)(-1) = 5(-1)+7 = -5+7 = 2 \] Therefore, \( (f \circ g)(-1) = 2 \). d. To find \( (g \circ f)(-1) \), we substitute \( x = -1 \) into the expression for \( (g \circ f)(x) \): \[ (g \circ f)(-1) = 5(-1)+15 = -5+15 = 10 \] Therefore, \( (g \circ f)(-1) = 10 \).