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If f(x) = x2 – 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1). |
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Answer» Given as f(x) = x2 – 3x + 4. Let us find the x satisfying f (x) = f (2x + 1). Here, we have, f(2x + 1) = (2x + 1)2 – 3(2x + 1) + 4 = (2x) 2 + 2(2x) (1) + 12 – 6x – 3 + 4 = 4x2 + 4x + 1 – 6x + 1 = 4x2 – 2x + 2 Then, f (x) = f (2x + 1) x2 – 3x + 4 = 4x2 – 2x + 2 4x2 – 2x + 2 – x2 + 3x – 4 = 0 3x2 + 3x – 2x – 2 = 0 3x(x + 1) – 2(x + 1) = 0 (x + 1)(3x – 2) = 0 x + 1 = 0 or 3x – 2 = 0 x = –1 or 3x = 2 x = –1 or 2/3 Thus, the values of x are –1 and 2/3. |
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