Q. 14.9( 14 Votes )

If f(x) = x2

Answer :

Given f(x) = x2 – 3x + 4.


We need to find x satisfying f(x) = f(2x + 1).


We have f(2x + 1) = (2x + 1)2 – 3(2x + 1) + 4


f(2x + 1) = (2x)2 + 2(2x)(1) + 12 – 6x – 3 + 4


f(2x + 1) = 4x2 + 4x + 1 – 6x + 1


f(2x + 1) = 4x2 – 2x + 2


Now, f(x) = f(2x + 1)


x2 – 3x + 4 = 4x2 – 2x + 2


3x2 + x – 2 = 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


Thus, the required values of x are –1 and.


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