Matematika

Pertanyaan

Diketahui f(x) = 2x/x - 1 dan g(x) = 2x + 1. Tentukan:
a. (f o g) (x)
b. (f o g) (-2)

1 Jawaban

  • 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

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