Jawaban:
a. 100x² + 360x + 318
b. 20x² - 21
Ingat!
(f ∘ g)(x) = f(g(x))
(g ∘ f)(x) = g(f(x))
Pembahasan:
f(x) = 4x² - 6
g(x) = 5x + 9
a. (f ∘ g)(x)
= f(g(x))
= f(5x + 9)
= 4(5x + 9)² - 6
= 4(25x² + 90x + 81) - 6
= 100x² + 360x + 324 - 6
= 100x² + 360x + 318
Dengan demikian diperoleh fungsi (f ∘ g)(x) = 100x² + 360x + 318
b. (g ∘ f)(x)
= g(f(x))
= g(4x² - 6)
= 5(4x² - 6) + 9
= 20x² - 30 + 9
= 20x² - 21
Dengan demikian diperoleh fungsi (g ∘ f)(x) = 20x² - 21
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Jawaban:
Jawaban:
a. 100x² + 360x + 318
b. 20x² - 21
Ingat!
(f ∘ g)(x) = f(g(x))
(g ∘ f)(x) = g(f(x))
Pembahasan:
f(x) = 4x² - 6
g(x) = 5x + 9
a. (f ∘ g)(x)
= f(g(x))
= f(5x + 9)
= 4(5x + 9)² - 6
= 4(25x² + 90x + 81) - 6
= 100x² + 360x + 324 - 6
= 100x² + 360x + 318
Dengan demikian diperoleh fungsi (f ∘ g)(x) = 100x² + 360x + 318
b. (g ∘ f)(x)
= g(f(x))
= g(4x² - 6)
= 5(4x² - 6) + 9
= 20x² - 30 + 9
= 20x² - 21
Dengan demikian diperoleh fungsi (g ∘ f)(x) = 20x² - 21