Matematika

Pertanyaan

Jika f(x)=2x-1, g(x)=7+3x, dan h(x)= 5x, carilah:
a) (f-1 o g-1 o h-1 ) (x)
b) (f o g o h)-1 (x)

Tolong dijawab yaa

1 Jawaban

  • cari inversnya satu satu
    f(x) = 2x-1
    y=2x-1
    2x=y+1
    x=(y+1)/2
    f-1(x)=(x+1)/2

    g(x)=7+3x
    y=7+3x
    3x=y-7
    x=(y-7)/3
    g-1(x)=(x-7)/3

    h(x)=5x
    y=5x
    x=y/5
    h-1(x)=x/5

    f-1 o g-1 o h-1 (x) = f-1(g-1(h-1(x)))
    =f-1(g-1(x/5))
    =f-1(((x/5)-7)/3)
    samakan penyebut
    =f-1((x-35)/5 x 1/3)
    =f-1((x-35)/15)
    =(((x-35)/15)+1)/2
    samakan penyebut
    =(x-20)/15 x 1/2
    =(x-20)/30

    (fogoh)-1(x)
    =h-1 o g-1 o f-1(x)
    =h-1 (g-1 ((x+1)/2))
    =h-1((((x+1)/2)-7)/3)
    =h-1((x-13)/6)
    =(x-13)/30

    maaf jika ada kesalahan

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