Exercise: Find (fo g) and (go f). Given f(x) = 3x + 1 and g(x) = x+7solutions
Answer (1)
Answer:(f o g)(x)Find g(x): g(x) = x + 7Substitute g(x) into f(x): f(g(x)) = f(x + 7) = 3(x + 7) + 1Simplify: 3x + 21 + 1 = 3x + 22Therefore, (f o g)(x) = 3x + 22(g o f)(x)Find f(x): f(x) = 3x + 1Substitute f(x) into g(x): g(f(x)) = g(3x + 1) = (3x + 1) + 7Simplify: 3x + 1 + 7 = 3x + 8Therefore, (g o f)(x) = 3x + 8
