Matematika

Pertanyaan

jika f(x) =1 per x dan g(x) = 2x - 1 maka (fog) negatif 1(x) =

2 Jawaban

  • g invers = (x+1)/2
    f invers = 1/x
    fog invers = g invers o f invers = ((1/x)+1)/2 = ((1+x)/x)/2

  • f(x) = 1/x
    g(x) = 2x - 1
    (f o g)(x) = f(g(x)) = 1/g(x) = 1/(2x - 1)
    1/(2x - 1) = y
    2xy - y = 1
    2xy = y + 1
    x = (y + 1)/(2y)
    (f o g)^-1(x) = (x + 1)/(2x)

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