Diketahui f(x) = 2x/x - 1 dan g(x) = 2x + 1. Tentukan: a. (f o g) (x) b. (f o g) (-2)
Matematika
yatu
Pertanyaan
Diketahui f(x) = 2x/x - 1 dan g(x) = 2x + 1. Tentukan:
a. (f o g) (x)
b. (f o g) (-2)
a. (f o g) (x)
b. (f o g) (-2)
1 Jawaban
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1. Jawaban ARCOLD
A. (f•g)(x)
= f (x²-2x+2)
= 2(x²-2x+2) + 1
= 2x²-4x+4+1
= 2x²-4x+5
b. (g•f)(x)
= g (2x+1)
= (2x+1)² - 2(2x+1) + 2
= 4x²+4x+1 -4x -2+2
= 4x²+ 1
c. (g•g)(x)
= g (x²-2x+2)
= (x²-2x+2)²-2(x²-2x+2) +2
= x⁴-4x³+6x²-6x+4
d. (f•f)(x)
= f (2x+1)
= 2(2x+1) + 1
= 4x+2+1
= 4x+3
e. (g•f)(-2) = 4x²+1
= 4*(-2)²+1
= 4*4+1
= 17