Matematika

Pertanyaan

Dik f(x-2)=x pangkat2 +4x-7. Invers fungsi f(x) adalah.........

1 Jawaban

  • f(x-2) = x² + 4x - 7
    f(x-2) = (x-2)² + 8(x-2) + 5

    dengan (x-2) = x , maka:
    f(x) = x² + 8x + 5
    y = x² + 8x + 5
    x² + 8x + (5 - y) = 0

    pakai rumus abc :
    x1,2 = [-b +- √(b² - 4ac)]/2a
    x1,2 = [-8 +- √(64 - 4(5 - y)]/2
    x1,2 = [-8 +- √(44 - 4y)] / 2
    x1,2 = [ -8 +- 2√(11-y)]/2
    x1,2 = -4 +- √(11 - y)

    adapun inversnya :
    x1 = -4 + √(11 - y)
    f(x) invers = -4 + √(11 - x)

    x2 = -4 - √(11-y)
    f(x) invers = -4 - √(11 - x)

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