Matematika

Pertanyaan

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ada yg bisa mengerjakan ini? #mohonBantuannya #ありがとうございます nanti saya follow

1 Jawaban

  • No. 5 A
    [tex]y = \frac{2x}{x+4} \\ y = \frac{2}{1 + \frac{4}{x}} \\ 1+\frac{4}{x} = \frac{2}{y} \\ \frac{4}{x} = \frac{2}{y} - 1 \\ \frac{4}{x} = \frac{2 - y}{y} \\ x = \frac{4y}{2-y} \\ f^{-1}(y) = \frac{4y}{2-y} \\ f^{-1}(x) = \frac{4x}{2-x} \\[/tex]

    No. 5B
    [tex]y = \frac{x-2}{2x+5}\\ y(2x+5) = x-2\\ 2xy + 5y = x - 2 \\ 2xy - x = -5y - 2 \\ x(2y - 1) = -5y - 2 \\ x = -\frac{5y+2}{2y-1} \\ g^{-1}(y) = -\frac{5y+2}{2y-1} \\ g^{-1}(x) = -\frac{5x+2}{2x-1} \\[/tex]

    No. 5C
    [tex]y = \frac{4x}{2-x} \\ y(2-x) = 4x \\ 2y - xy = 4x \\ 4x + xy = 2y \\ x(4+y) = 2y \\ x = \frac{2y}{4+y}\\ f^{-1}\left ( f^{-1}(y)\right ) = \frac{2y}{4+y} \\ f^{-1}\left ( f^{-1}(x)\right ) = \frac{2x}{4+x}[/tex]

    No. 5D
    [tex]y = -\frac{5x+2}{2x-1} \\ y(2x-1) = -5x-2 \\ 2xy - y = -5x-2 \\ 2xy + 5x = y - 2 \\ x(2y + 5) = y - 2 \\ x = \frac{y - 2}{2y + 5} \\ g^{-1}\left ( g^{-1}(y)\right ) = \frac{y - 2}{2y + 5} \\ g^{-1}\left ( g^{-1}(x)\right ) = \frac{x - 2}{2x + 5} \\ [/tex]

    No. 5E
    Apabila fungsi invers [tex]f[/tex] diinverskan, maka hasilnya adalah fungsi [tex]f[/tex] itu sendiri, atau secara matematis

    [tex]f^{-1}\left ( f^{-1}(x)\right ) = f(x)[/tex]