[tex]f:\mathbb{R}\to \mathbb{R}[/tex]
[tex]\begin{aligned}f(x) &= x^2-x+2 \\ &=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}+2\\ &=\left(x-\frac{1}{2}\right)^2+\frac{7}{4}\end{aligned}[/tex]
[tex]\text{Dar}\,\left(x-\frac{1}{2}\right)^2 \geq 0 \Rightarrow \left(x-\frac{1}{2}\right)^2+\frac{7}{4} \geq \frac{7}{4} \\ \\\Rightarrow f(x)\geq \frac{7}{4}\Rightarrow \text{Imf} = \left[\frac{7}{4},+\infty\right)[/tex]
