if f(x)=x^2+3 find x if f(x)=f(2x+1)
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Solution :
Given f(x) = x² + 3 -----( 1 )
f(2x+1) = (2x+1)² + 3
= (2x)²+2*2x*1+1² + 3
= 4x²+4x+4 ----( 2 )
According to the problem,
f(2x+1) = f(x)
=> 4x²+4x+4 = x² + 3
=> 3x² + 4x + 1 = 0
=> 3x² + 3x + 1x + 1 = 0
=> 3x( x + 1 ) + 1( x + 1 ) = 0
=> ( x + 1 )( 3x + 1 ) = 0
Therefore ,
x + 1 = 0 or 3x + 1 = 0
x = -1 or x = -1/3
•••••
Given f(x) = x² + 3 -----( 1 )
f(2x+1) = (2x+1)² + 3
= (2x)²+2*2x*1+1² + 3
= 4x²+4x+4 ----( 2 )
According to the problem,
f(2x+1) = f(x)
=> 4x²+4x+4 = x² + 3
=> 3x² + 4x + 1 = 0
=> 3x² + 3x + 1x + 1 = 0
=> 3x( x + 1 ) + 1( x + 1 ) = 0
=> ( x + 1 )( 3x + 1 ) = 0
Therefore ,
x + 1 = 0 or 3x + 1 = 0
x = -1 or x = -1/3
•••••
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