Jika diberikan f (x)= (2x-3) dan g (x)= x^2 tentukanlah A) (FoG)(x) B) (FoG)^-1 (2)
Matematika
Salsaam11
Pertanyaan
Jika diberikan f (x)= (2x-3) dan g (x)= x^2 tentukanlah
A) (FoG)(x)
B) (FoG)^-1 (2)
A) (FoG)(x)
B) (FoG)^-1 (2)
1 Jawaban
-
1. Jawaban ahreumlim
f(x) = 2x - 3
g(x) = x²
(fog)(x)
= f(g(x))
= f(x²)
= 2x² - 3
(fog)⁻¹(x)
misal
y = 2x² - 3
y + 3 = 2x²
x² = (y + 3) / 2
x = +-√[(y + 3) / 2]
jadi
utk x ≥ 0,
(fog)⁻¹(x) = √[(x + 3) / 2]
maka
(fog)⁻¹(2)
= √[(2 + 3) / 2]
= √(5/2)