Question

Dadas as funções F (x) = 3x +2 e G (x) = x-4 encontre as funções compostas

A) F (g (x) ) =

B) G (f (x) ) =

C) F (f (-1) ) =

D) F (f (2) ) / G (g (6) ) =

Answer 1

a)

$f(g(x)) = 3.g(x) + 2 = 3.(x - 4) + 2 = 3x - 12 + 2 = 3x - 10$

b)

$g(f(x)) = f(x) - 4 = 3x + 2 - 4 = 3x - 2$

c)

$f( - 1) = 3.( - 1) + 2 = - 3 + 2 = - 1 \\ f(f( - 1)) = f( - 1) = - 1$

d)

$f(2) = 3.2 + 2 = 6 + 2 = 8 \\ f(f(2)) = 3.8 + 2 = 24 + 2 = 26 \\ g(6) = 6 - 4 = 2 \\ g(g(6)) = 2 - 4 = - 2 \\ \frac{f(f(2))}{g(g(6))} = \frac{26}{ - 2} = - 13$