a)
[tex]\it x^2-4x+10=x^2-4x+4+6=(x-2)^2+6 \geq6 \Rightarrow \\ \\ \Rightarrow numitorul\ frac\c{\it t}iei\ este\ diferit \ de\ 0\ pentru\ oricare\ x\in\mathbb{R}[/tex]
Deci, expresia este definită pentru oricare x număr real.
b)
[tex]\it x^2-4x+10\geq6 \Rightarrow\dfrac{1}{x^2-4x+10}\leq\dfrac{1}{6}|_{\cdot6}\Rightarrow\dfrac{6}{x^2-4x+10}\leq1 \Rightarrow\\ \\ \\ \Rightarrow 0< \dfrac{6}{x^2-4x+10}\leq1|_{+5} \Rightarrow 5< 5+\dfrac{6}{x^2-4x+10}\leq6 \Rightarrow E(x)\in(5,\ 6][/tex]
c)
[tex]\it E(x)\in (5,\ 6] \Rightarrow [E(x) ] \in\{5,\ 6\}[/tex]
d)
[tex]\it [E(x)]=6\ dac\breve{a}\ \dfrac{6}{x^2-4x+10}=1 \Rightarrow x^2-4x+10=6 \Rightarrow\\ \\ \\ \Rightarrow x^2-4x+4=0 \Rightarrow(x-2)^2=0 \Rightarrow x-2=0 \Rightarrow x=2[/tex]
