Matematika Sekolah Menengah Atas KUIS Diketahui bahwa f(x+3) = x²-5x+6 Tentukan f(x)

jeremiekossulv – March 07, 2023

KUIS
Diketahui bahwa
f(x+3) = x²-5x+6
Tentukan f(x)

Misal:

x + 3 = a

x = a - 3

f(a) = a² - 5a + 6

= (a - 3)² - 5 (a - 3) + 6

= a² - 6a + 9 - 5a + 15 + 6

= a² - 11a + 30

f(x) = x² - 11x + 30

Penjelasan dengan langkah-langkah:

f(x+3) = x² – 5x + 6

f(g(x)) = x² – 5x + 6

g(x) = x + 3

misal g(x) = y

maka, y = x + 3

–x = –y + 3

x = y – 3

g-¹(x) = x – 3

f(g(x)) = x² – 5x + 6

f(g(x)) = (x – 2)(x – 3)

f(x) = (g-¹(x) – 2)(g-¹(x) – 3)

f(x) = (x –3 –2)(x –3 –3)

f(x) = (x – 5)(x – 6)

f(x) = x(x – 6) – 5(x – 6)

f(x) = x² – 6x – 5x + 30

f(x) = x² – 11x + 30

[answer.2.content]