a)Tìm hàm số f(x) biết f(x+1) = x2 –x +2 b)Tìm hàm số f(x) biết f(x-2) = x2 -2x +
2 câu trả lời
a) ` f ( x + 1 ) = x^2 - x + 2 `
` f ( x + 1 ) = x^2 + x + x + 1 - 3x + 1 `
` f ( x + 1 ) = ( x^2 + x ) + ( x + 1 ) - 3x - 3 + 4 `
` f ( x + 1 ) = x ( x + 1 ) + ( x + 1 ) - ( 3x + 3 ) + 4 `
` f ( x + 1 ) = ( x + 1 ) ( x + 1 ) - 3 ( x + 1 ) + 4 `
` f ( x + 1 ) = ( x + 1 )^2 - 3 ( x + 1 ) + 4 `
Suy ra ` f ( x ) = x^2 - 3x + 4 `
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b) ` f ( x - 2 ) = x^2 - 2x + 3 `
` f ( x - 2 ) = x^2 - 2x - 2x + 4 + 2x - 1 `
` f ( x - 2 ) = ( x^2 - 2x ) - ( 2x - 4 ) + 2x - 4 + 3 `
` f ( x - 2 ) = x ( x - 2 ) - 2 ( x - 2 ) + 2 ( x - 2 ) + 3 `
` f ( x - 2 ) = ( x - 2 ) ( x - 2 ) + 2 ( x - 2 ) + 3 `
` f ( x - 2 ) = ( x - 2 )^2 + 2 ( x - 2 ) + 3 `
Suy ra ` f ( x ) = x^2 + 2x + 3 `
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