f(x) = x+2 and g(x) = 5x2-4

Question

find the following and simplylify completey.

Answer 1

x+2 and 5x^2-4

f(x) = x+2 g(x)= 5x^2 - 4

has several standard problems

f(g(x)) or g(f(x)) or (f+g)(x) or (f-g)(x)

for f(g(x)) = f(5x^2-4) = 5x^2 -4 + 2 = 5x^2 -2

for g(f(x)) = g(x+2) = 5(x+2)^2 -4 = 5(x^2 +4x+4) -4 = 5x^2 + 20x + 20 - 4 = 5x^2 + 20x +16

(f+g)(x) = f(x) + g(x) = x+2 + 5x^2 -4 = 5x^2 + x -2

(f-g)(x) = f(x) - g(x) = x+2 -5x^2 +4 = -5x^2 +x +6