g(x)=x²-1
h(x)=3x
Tentukan:
a. (hogof)(x)
b. (hogof)(8)
c. (fogoh)(x)
d. (fogoh)(8)
pakai cara secara rinci!
SOAL A.
(hogof)(x) = h(g(f(x)))
(hogof)(x) = h(g(2 + x))
(hogof)(x) = h((2 + x)² - 1)
(hogof)(x) = h((x² + 4x + 4) - 1)
(hogof)(x) = h(x² + 4x + 4 - 1)
(hogof)(x) = h(x² + 4x + 3)
(hogof)(x) = 3(x² + 4x + 3)
(hogof)(x) = 3x² + 12x + 9
SOAL B.
(hogof)(x) = h(g(f(x)))
(hogof)(x) = h(g(2 + x))
(hogof)(x) = h((2 + x)² - 1)
(hogof)(x) = h((x² + 4x + 4) - 1)
(hogof)(x) = h(x² + 4x + 4 - 1)
(hogof)(x) = h(x² + 4x + 3)
(hogof)(x) = 3(x² + 4x + 3)
(hogof)(x) = 3x² + 12x + 9
(hogof)(8) = 3•(8)² + 12•8 + 9
(hogof)(8) = 3•64 + 96 + 9
(hogof)(8) = 192 + 105
(hogof)(8) =297
SOAL C.
(fogoh)(x) = f(g(h(x)))
(fogoh)(x) = f(g(3x))
(fogoh)(x) = f((3x)² - 1)
(fogoh)(x) = f(9x² - 1)
(fogoh)(x) = 2 + (9x² - 1)
(fogoh)(x) = 2 + 9x² - 1
(fogoh)(x) = 9x² + 2 - 1
(fogoh)(x) = 9x² + 1
SOAL D.
(fogoh)(x) = f(g(h(x)))
(fogoh)(x) = f(g(3x))
(fogoh)(x) = f((3x)² - 1)
(fogoh)(x) = f(9x² - 1)
(fogoh)(x) = 2 + (9x² - 1)
(fogoh)(x) = 2 + 9x² - 1
(fogoh)(x) = 9x² + 2 - 1
(fogoh)(x) = 9x² + 1
(fogoh)(8) = 9•(8)² + 1
(fogoh)(8) = 9•64 + 1
(fogoh)(8) = 576 + 1
(fogoh)(8) = 577
[answer.2.content]
