Question

Sejam as funções f(x)=3x e g(x)=5x+2, determine:

B) f(g(2)) - g(g(1))
C) f(g(x))
D) g(f(x))
E) fof
F) gog

Answer 1

b) g(2) = 5×2 + 2 ⇒ 12. g(1) = 5×1 + 2 ⇒ 7. f(g(2)) ⇒ f(12) = 3×12 ⇒ 36. g(g(1)) ⇒ g(7) = 5×7 + 2 ⇒ 37. f(g(2)) - g(g(1)) = 36 - 37 = -1.

c) f(g(x)) ⇒ f(5x + 2) ⇒ 3×(5x + 2) ⇒ 15x +6.

d) g(f(x)) ⇒ g(3x) ⇒ 5×3x + 2 ⇒ 15x + 2.

e) fof = f(f(x)) ⇒ f(3x) ⇒3×3x ⇒ 9x.

f) gog = g(g(x)) ⇒ g(5x + 2) ⇒ 5×(5x + 2) + 2 ⇒ 25x + 10 + 2 ⇒ 25x + 12.