Question

If $f\left(x\right)=x^2-3x+4$, then find the value of x satisfying $f\left(x\right)=f(2x+1).$

Answer 1

$f(2x+1)=(2x+1{)}^2-3(2x+1)+4=4x^2-2x+2$

For,
$f\left(x\right)=f(2x+1)\Rightarrow x^2-3x+4=4x^2-2x+2$

$\Rightarrow 3x^2+x-2=0$

$\Rightarrow 3x^2+3x-2x-2=0$

$\Rightarrow (3x-2)(x+1)=0$

$\Rightarrow x=-1,\frac{2}{3}$