Matematika

Pertanyaan

tentukan invers fungsi dibawah ini=
a) f(x)= 3x^2+4/2x^2-5
b) f(x)=(1-x^3)^1/5
c)f(x)=2x+5/x-1

1 Jawaban

  • a) f(x)= 3x^2+4/2x^2-5
    y = 3x^2+4/2x^2-5
    y(2x²-5)=3x²+4
    2x²y - 5y = 3x²+4
    2x²y-3x²= 5y+4
    x²(2y-3)=5y+4
    x²=5y + 4 / 2y-3
    x = √( 5y + 4 / 2y-3)
    f-¹(x) = √(5x+4 / 2x-3)

    b) f(x)=(1-x^3)^1/5
    y= (1-x^3)^1/5
    y^5 = 1-x³
    x³= 1-y^5
    x = (1-y^5)^1⅓
    f-¹(x) = (1-x^5)^⅓

    c)f(x)=2x+5/x-1
    y = 2x+5/x-1
    y(x-1)=2x+5
    xy-y=2x+5
    xy-2x=y+5
    x(y-2)=y+5
    f-¹(x) = x+5 / x-2

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