g(x) = x+1 (fog)(x) = 6x²+12x+5 tentukan f(x)
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[tex](fog)(x) = {6x}^{2} + 12x + 5[/tex]
[tex]f(g(x)) = {6x}^{2} + 12x + 5[/tex]
[tex]f(x + 1) = {6x}^{2} + 12x + 5[/tex]
Misalkan, y = (x + 1). Maka x = (y - 1). Sehingga,
[tex]f(y) = 6 \: {(y - 1)}^{2} + 12 \: (y - 1) + 5[/tex]
[tex]f(y) = 6 \: ({y}^{2} - 2y + 1) + 12y - 12 + 5[/tex]
[tex]f(y) = {6y}^{2} - 12y + 6 + 12y - 12 + 5[/tex]
[tex]f(y) = {6y}^{2} - 12y + 12y + 6 - 12 + 5[/tex]
[tex]f(y) = {6y}^{2} + 6 - 12 + 5[/tex]
[tex]f(y) = {6y}^{2} - 1[/tex]
Ubahlah kembali variabel y, menjadi variabel x. Sehingga,
[tex]f(x) = {6x}^{2} - 1[/tex]
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