Show your work Clearly explain all steps Simplify your answe

Show your work. Clearly explain all steps. Simplify your answers if possible. Let f(x) = 3x + 1 and g(x) = x^2 + 2x + 5. Find: f(g(x)) = g(f(x) =

Solution

f(x)=3x+1 and g(x)= x^2 + 2x+5

a) f(g(x))= f(x^2 + 2x+5)= 3(x^2 + 2x+5) +1=3x^2 + 6x+16

b) g(f(x))=g(3x+1)= (3x+1)^2 + 2(3x+1)+5= 9x^2 + 6x+1+ 6x+ 2+5= 9x^2 + 12x+ 8