Matematika

Pertanyaan

nomor 1 sampe nomor 5 itu kayamana yaaaaaaa
nomor 1 sampe nomor 5 itu kayamana yaaaaaaa

1 Jawaban


  • [tex]3) \: log_{2}(x - 6) + log_{2}(x + 3) > log_{2}(- x + 30) \\ log_{2}( {x}^{2} - 3x - 18) > log_{2}( - x + 30) \\.. \: {x}^{2} - 3x - 18 > 0 \\ maka \: (x - 6)(x + 3) > \: 0 \: \: \: \: x > 6 \: atau \: x < - 3 \\ ..( - x + 30) > 0 \\ maka \: x < 30 \\ {x}^{2} - 3x - 18 > - x + 30 \\ {x}^{2} - 2x - 48 > 0 \\ (x - 8)(x + 6) > 0 \\ x > 8 \\ x < - 6 \\ irisannya \: adalah \: \: 8 < x < 30[/tex]
    [tex]4) \: \: (fog)(x) = {(2x - 3)}^{2} - 2(2x - 3) + 5 \\ = 4 {x}^{2} - 12x + 9 - 4x + 6 + 5 \\ = 4 {x}^{2} - 16x + 20[/tex]
    [tex]5) \: \: (gof)(x) = \frac{3x + 8}{3x + 8 - 4} = \frac{3x + 8}{3x + 4} = y \\maka \: \frac{3y + 8}{3y + 4} = x \\3xy + 4x = 3y + 8 \\ 4x - 8 = 3y - 3xy \\ 4x - 8 = (3 - 3x)y \\ y = {(gof)}^{ - 1} (x) = \frac{4x - 8}{3 - 3x} [/tex]