Question

Dadas as funções f(x) = 5x-8, g(x)= x² - 4x, determine:
a) fg((x))

b) g(f(x)

Answer 1

f(x) = 5x - 8
g(x) = x² - 4x

f(g(x))

g(x) = x² - 4x

f(x) = 5x - 8
f(x² - 4x) = 5 . (x²- 4x) - 8
f(x² - 4x) = 5x² - 20x - 8

f(g(x)) = 5x² - 20x - 8

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g(f(x))

f(x) = 5x - 8

g(x) = x² - 4x

g(f(x)) = (5x - 8)² - 4 . (5x - 8)

g(f(x)) = 25x² - 80x + 64 - 20x + 32

g(f(x)) = 25x² - 100x + 96