Question

Acest exercitiu, va rog!

Answer 1

$f:\mathbb{R}\to \mathbb{R}$

$\begin{aligned}f(x) &= x^2-x+2 \\ &=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}+2\\ &=\left(x-\frac{1}{2}\right)^2+\frac{7}{4}\end{aligned}$

$\text{Dar}\,\left(x-\frac{1}{2}\right)^2 \geq 0 \Rightarrow \left(x-\frac{1}{2}\right)^2+\frac{7}{4} \geq \frac{7}{4} \\ \\\Rightarrow f(x)\geq \frac{7}{4}\Rightarrow \text{Imf} = \left[\frac{7}{4},+\infty\right)$

Answer 2

la sfarsit e intervalul 7/4,infinit(daca nu se intelege.