Question

Find the range of the following functions:
$f\left(x\right)=\sqrt{x^2-x+1}$

Answer 1

$f\left(x\right)=\sqrt{x^2-x+1}$

$f\left(x\right)=\sqrt{(x-\frac{1}{2}{)}^2-x+3/4}$

So, $Min\left(f\right(x\left)\right)=\frac{3}{\sqrt{2}}$

At $x=\frac{1}{2}$

And $Max\left(f\right(x\left)\right)=\infty$

So, range$⟹(\frac{\sqrt{3}}{2},\infty )$