Question

dadas as funções f(x)=3x+3 e g(x)=4x-2 caucule:

a)f(g(x) )

b)g(f(x) )

c)f ( g(-1 ) )

d)g( f(4 ) )

e)f(g (3 ) )

f)g(f (-2 ) )​

Answer 1

Explicação passo-a-passo:

a) f(g(x)) → f(4x - 2) = 3 (4x - 2) + 3 = 12x - 6 + 3 = 12x - 3

                f(g(x)) = 12x - 3

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b) g(f(x)) → g(3x + 3) = 4 (3x + 3) - 2 = 12x + 12 - 2 = 12x + 10

                 g(f(x)) = 12x + 10

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c) f(g(-1)) → g(-1) = 4 . (-1) - 2 → g(-1) = -4 - 2 → g(-1) = -6

                 f(g(-1)) = f(-6) = 3 . (-6) + 3 → f(-6) = -18 + 3 → f(-6) = -15

                 f(g(-1)) = -15

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d) g(f(4)) → f(4) = 3 . 4 + 3 → f(4) = 12 + 3 → f(4) = 15

                 g(f(4)) = g(15) = 4 . 15 - 2 → g(15) = 60 - 2 → g(15) = 58

                 g(f(4)) = 58

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e) f(g(3)) → g(3) = 4 . 3 - 2 → g(3) = 12 - 2 → g(3) = 10

                 f(g(3)) = f(10) = 3 . 10 + 3 → f(10) = 30 + 3 → f(10) = 33

                 f(g(3)) = 33

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f) g(f(-2)) → f(-2) = 3 . (-2) + 3 → f(-2) = -6 + 3 → f(-2) = -3

                 g(f(-2)) = g(-3) = 4 . (-3) - 2 → g(-3) = -12 - 2 → g(-3) = -14

                 g(f(-2)) = -14