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if f(x) = x² - 3x +4, find the value of x satisfying f(x) = f(2x +1). |
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Answer» here the value of x is =-1 or 2/3 Given:f (x) = x2 – 3x + 4Therefore,f (2x + 1) = (2x + 1)2 – 3(2x + 1) + 4 = 4x2 + 1 + 4x – 6x – 3 + 4 = 4x2 – 2x + 2Now,f (x) = f (2x + 1)⇒ x2 – 3x + 4 = 4x2 – 2x + 2⇒ 4x2 – x2 – 2x + 3x + 2 – 4 = 0⇒ 3x2 + x – 2 = 0⇒ 3x2 + 3x – 2x – 2 = 0⇒ 3x(x + 1) – 2(x +1) = 0⇒ (3x – 2)(x +1) = 0⇒ (x + 1) = 0 or ( 3x – 2) = 0⇒x=−1 or x=23⇒x=-1 or x=23Hence, x=−1,23x=-1,23. |
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