Matematika

Pertanyaan

Diketahui :
f(x)= x pangkat 2
g(x)=1/x
h(x)=x+1
i(x)= x pangkat 2 -8x+10

Tentukanlah :
A.) fogoh (x)
B.) Fogoh (0)
C.) ( i )-1 (x)

1 Jawaban

  • A.) (f o g o h) (x) = f o g (h (x))
    ============> = f o g (x + 1)
    ============> = f (g (x + 1))
    ============> = f(1 / (x+1))
    ============> = (1 / x+1)^2
    ============> = (1 / x+1) (1 / x+1)
    ============> = 1 / (x^2 + 2x + 1)

    B.) (f o g o h) (0) = 1 / ((0)^2 + 2(0) + 1)
    ============> = 1 / 1 = 1

    C.) (i)^-1 (x)
    y = i(x)
    y = x^2 - 8x + 10
    y -10 = x^2 - 8x
    y - 10 = x (x - 8)
    x = (y - 10) / (x - 8)
    (i)^-1 (x) = (x - 10) / (x - 8)

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