Question

Determinaţi mulţimea valorilor funcţiei f:R=>R , f(x)=x^2+x+1

Answer 1

$\it f(x)=x^2+x+1=x^2+x+\dfrac{1}{4}+\dfrac{3}{4}=(x+\dfrac{1}{2})^2+\dfrac{3}{4} \Rightarrow f(x)\geq\dfrac{3}{4},\ \forall x\in\mathbb{R}\\ \\ Imf=\Big[\dfrac{3}{4},\ \infty\Big)$