Matematika

Pertanyaan

diketahui fungsi f(x)= x^2-2,g(x-1)=2x-1 dan h(x+1)=6-x. Nilai (fogoh)(2) adalah...

1 Jawaban

  • f(x) = x^2 - 2

    g(x - 1) = 2x - 1 => misal x - 1 = a maka x = a + 1
    g(a) = 2(a + 1) - 1 = 2a + 2 - 1 = 2a + 1
    g(x) = 2x + 1
    => g(5) = 2(5) + 1 = 11

    h(x + 1) = 6 - x => misal x + 1 = a maka x = a - 1
    h(a) = 6 - (a - 1) = 6 - a + 1 = 7 - a
    h(x) = 7 - x
    => h(2) = 7 - 2 = 5

    (f o g o h)(2) = (f o g)(h(2)) = (f o g)(5) = f(g(5)) = f(11) = 11^2 - 2 = 121 - 2 = 119

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