Question

4. Sejam as funções f(x) = x2 – 2x + 1 e g(x) = 2x + 1.
Calcule:
a) f(g(1))
b) g(f(-2))

Answer 1

Sejam as funções:
f(x) = x^2 – 2x + 1
g(x) = 2x + 1
Calcule:
g(x) = 2x + 1
F(x)= x^2 - 2x + 1
F[g(x)]
(X)^2 - 2(x) + 1
= (2x+1)^2 - 2.(2x+1) + 1
= (2.1+1)^2 - 2.(2.1+1) + 1
= (2+1)^2 - 2.(2+1) + 1
= 3^2 - 2.3 + 1
= 9 - 6 + 1
= 4

a) f(g(1)) = 4

= (2x+1)^2 - 2.(2x+1) + 1
= (2.1+1)^2 - 2.(2.1+1) + 1
= (2+1)^2 - 2.(2+1) + 1
= 3^2 - 2.3 + 1
= 9 - 6 + 1
= 4

___________

g(x) = 2x + 1
F(x)= x^2 - 2x + 1
G[f(x)] = 2.(x^2 - 2x + 1) + 1
G[f(x)]= 2x^2 - 4x + 2 + 1
G[f(x)] = 2x^2 - 4x + 3
G[f(-2)] = 2.(-2)^2 - 4.(-2) + 3
G[f(-2)]= 2.4 + 8 + 3 = 8+11= 19

b) g(f(-2)) = 19
G[f(x)] = 2x^2 - 4x + 3
G[f(-2)] = 2.(-2)^2 - 4.(-2) + 3
G[f(-2)]= 2.4 + 8 + 3
G[f(2)] = 8+11
G[f(-2)] = 19