Question

Să se determine imaginea funcției $f : R$ ⇒ $R$, $f(x)= x^{2} -x+2$.

Answer 1

[tex]f:\mathbb{R}\rightarrow \mathbb{R},f(x)=x^2-x+2\\ Notam\ f(x)=y,y\in \mathbb{R}\\ x^2-x+2=y\\ x^2-x+2-y=0\\ \Delta=1-4(2-y)\\ \Delta=1-8+4y\\ \Delta=4y-7\\ Punem\ conditia\ \Delta\geq 0\\ 4y-7\geq 0\\ 4y\geq 7\\ y\geq \frac{7}{4}\Rightarrow y\in [\frac{7}{4},\infty)\\ Imf=[\frac{7}{4},\infty)[/tex]