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Question

If f(x)=x23x+4, then find the values of x satisfying the equation f(x)=f(2x+1).


Solution

We have,
f(x)=x23x+4
Now,
f(2x+1)=(2x+1)23(2x+1)+4
=4x2+1+4x6x3+4
=4x22x+2
It is given that
f(x)=f(2x+1)
x23x+4=4x22x+2
0=4x2x22x+3x+24
3x2+x2=0
3x2+3x2x2=0
3x(x+1)2(x+1)=0
(x+1)(3x2)=0
\Rightarrow x+1 = 0\) or 3x2=0
x=1 or x=23

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