Matematika

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Tolong bantu jawab no 3 sama 4 pake caranya lengkap *komposisi fungsi*
Tolong bantu jawab no 3 sama 4 pake caranya lengkap *komposisi fungsi*

1 Jawaban

  • jawab 
    3. 
    a. fog(x)  = f { g(x)} = f (-x - 2) = 3(-x-2)² + 1
    = 3(x² + 4x + 4 ) + 1
    = 3x² +12x + 13

    b. goh(-5) = g { h(-5)} = g {(1 +5 )/(-5+7)} = g (6/2)
    = g(3) = -3 - 2  
    = - 5

    4. 
    fog( 1/x - 1) = f { g(1/x -1)} = f(4 - (1/x  - 1))
    = f (4 -1/x + 1)
    = f (5 - 1/x)
    = (5 - 1/x) - 1)/ (5 - 1/x) 
    = (4 - 1/x) / (5 - 1/x)
    = (4x - 1)/(5x -1)

    b. gof(k) = 3 1/2 = 7/2
    g { f(k)} = g ((k -1)/k) 
    4 - (k - 1) /k  = 7/2
    (4k - k +1)/k = 7/2
    (3k + 1)/ k = 7/2
    7k = 2(3k +1)
    7k = 6k + 2
    k = 2