Question

dados as funções reais de variável real f(x) = 5x - 4 e g(x) = 3x + 6, determine:

a) (g o f)(2)

b) (f o g) (2

c) (f o f) (1)

d) (g o g) (3)

e) (g o f) (x)

f) (f o g) (x)

g) (f o f) (x)

h) (g o g) (x)

Answer 1

a) g(f(2)) = 5(2)-4 = 10-4 = 6

g(6)= 3(6)+6 = 18+6 = 24

b) f(g(2)) = 3(2)+6 = 6+6 = 12

f(12) = 5(12)-4= 60-4 = 56

c) f(f(1)) = 5(1)-4 = 5-4 = 1

f(1) = 5(1)-4 = 5-4 = 1

d) g(g(3)) = 3(3)+6 = 9+6 = 15

g(15) = 3(15)+6 = 45+6 = 51

e) g(f(x)) = 5(x)-4 = 5x-4

g(5x-4) = 3(5x-4)+6 = 15x-12+6 = 15x-6

f) f(g(x)) = 3(x)+6 = 3x+6

f(15x-6) = 5(3x+6)-4 = 15x+30-4 = 15x+26

g) f(f(x)) = 5(x)-4 = 5x-4

f(5x-4) = 5(5x-4)-4 = 25x-20-4 = 25x-24

h) g(g(x)) = 3(x)+6 = 3x+6

g(3x+6) = 3(3x+6)+6 = 9x+18+6 =9x+24