Matematika

Pertanyaan

1.dik: rumus f(x+7)=2x-5.tentukan rumus f(x)
2.jika f(2x-3)=10x-9,maka rumus f(x)adlh
3.dik: rumus f(x)=ax+b.jika f(2)=-2 dan f(-3)=13 maka nilai dr a+b

2 Jawaban

  • 1). f(x + 7) = 2x - 5
    f(x) = 2(x - 7) - 5
    f(x) = 2x - 14 - 5
    f(x) = 2x - 19
    2). f(2x - 3) = 10x - 9
    f(x) = 10(x + 3)/2 - 9
    f(x) = 5x + 15 - 9
    f(x) = 5x + 6
    3). f(2) = 2a + b = -2
    f(-3) = -3a + b = 13
    __________-
    5a = -15
    a = -15/5
    a = -3
    2a + b = -2
    2(-3) + b = -2
    -6 + b = -2
    b = 6 - 2
    b = 4
    Nilai a + b = -3 + 4 = 1
    4). f(x) = 3x + 4
    f(4) = a => 3(4) + 4 = a
    => 12 + 4 = a
    => 16 = a
    f(b) = -5
    f(b) = 3b + 4 = -5
    3b = -5 - 4
    3b = -9
    b = -9/3
    b = -3

    Nilai a+b = 16 + (-3) = 13


  • fungsi  komposisi
    1. f(x+7)= 2x - 5
    f(x)= 2(x-7) - 5
    f(x)= 2x -14 -5
    f(x)= 2x - 19

    2. f(2x-3) = 10x - 9
    f(x)= 10(x + 3)/2  - 9
    f(x)= 5(x+3) - 9
    f(x)= 5x +15 -9
    f(x)= 5x + 6

    3. f(X)= ax+b
    f(2)=  - 2
    f(-3) = 13
    ...
    2a - (-3a)= -2 - 13
    5a= -15
    a = - 3

    b = - 2 - 2a
    b = -2 -2(-3)
    b = -2+ 6  = 4

    a + b = -3 + 4
    a + b = 1

    4. f(x) =3x + 4
    f(4)= a --> 3(4)+ 4 = a
    12+4 = a --> a = 16

    f(b) =-5 --> 3b + 4 = - 5
    3b = - 5-4 = - 9
    b = -9 /3
    b = - 3

    a + b = 16 + (-3) 
    a + b = 13

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