Question

Find the domain and range of function y = √(−x^{2} −6x+2)

Answer 1

`y=√(-x^2-6x+2)\\\\D:-x^2-6x+2\geq0\\\\a=-1;\ b=-6;\ c=2\\\\\Delta=b^2-4ac;\ iff\ \Delta \geq0\ then\ x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\Delta=(-6)^2-4\cdot(-1)\cdot2=36+8=44;\ \sqrt\Delta=√(44)=√(4\cdot11)=2√(11)\\\\x_1=(6-2√(11))/(2\cdot(-1))=-3+√(11);\ x_2=(6+2√(11))/(2\cdot(-1))=-3-√(11)\\\\look\ at\ the\ picture\\\\D:x\in\left<-3-√(11);-3+√(11)\right>`