Matematika

Pertanyaan

fungsi f:R --> dan g:R --> dinyatakan oleh f(x)=x+2 dan (gof) (x)= 2x²+4x+1, maka g(x)

1 Jawaban

  • (g o f)(x) = 2x^2 + 4x + 1
    g(f(x)) = 2x^2 + 4x + 1
    g(x + 2) = 2x^2 + 4x + 1
    Misal x + 2 = a => x = a - 2
    g(a) = 2(a - 2)^2 + 4(a - 2) + 1
    g(a) = 2(a^2 - 4a + 4) + 4a - 8 + 1
    g(a) = 2a^2 - 8a + 8 + 4a - 8 + 1
    g(a) = 2a^2 - 4a + 1
    g(x) = 2x^2 - 4x + 1

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