Jika (fog)(x) =3x²-6x-1 dan g(x) =x²-2x+5 maka f(x) =…

(fog)(x) = 3x^2 -6x-1
g(x) = x^2 -2x +5
ditanya : f(x) ?
jawab
f(g(x)) = 3x^2 -6x -1
f(x^2 -2x +5) = 3x^2 -6x -1
misal
a = x^2 -2x +5
a-5 = x^2 -2x
a-5 + (-2/2)^2 = x^2 -2x + (-2/2)^2
a-5+1 = (x-1)^2
±√(a+4) = x -1
x1,2 = 1 ± √(a-4)
x1 = 1 + √(a-4)
x2 = 1 - √(a-4)

untuk x1 = 1 + √(a-4)
f(a) = 3(1 + √(a-4))^2 -6(1 + √(a-4)) -1
f(a) = 3(1^2 + 2√(a-4) + a-4) -6 -6√(a-4) -1
f(a) = 3(2√(a-4) + a -3) -6 -6√(a-4) -1
f(a) = 6√(a-4) +3a -9 -7 -6√(a-4)
f(a) = 3a -16
f(x) = 3x -16

untuk x2 = 1 - √(a-4)
f(a) = 3(1 - √a-4))^2 -6(1-√a-4)) -1
f(a) = 3(1^2 -2√(a-4) + a-4) -6 + 6√(a-4) -1
f(a) = 3(-3 -2√(a-4) + a ) -6 + 6√(a-4) -1
f(a) = -9 -6√(a-4) + 3a -7 + 6√(a-4)
f(a) = 3a -16
f(x) = 3x -16

maka f(x) = 3x -16

semoga bermamfaat dan membantu ;;)