f(x) = x²+3 Find x for which f(x) = f(2x + 1).
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Answer:
x is -1/3 and -1
Step-by-step explanation:
f(x) = x²+3
f(2x + 1) = (2x + 1)² + 3
= 4x² + 1 + 4x + 3
= 4x² + 4x + 4
f(x) = f(2x + 1)
x² + 3 = 4x² + 4x + 4
4x² - x² + 4x +4 - 3 = 0
3x² + 4x + 1 = 0
3x² + 3x + x + 1 = 0
3x(x + 1)+1(x + 1) = 0
(3x + 1)(x + 1) = 0
3x + 1 = 0 ; x + 1 = 0
3x = -1 ; x = -1
x = -1/3 ;x = -1
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