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

Sagot :

[tex]y=\sqrt{-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=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\Delta=(-6)^2-4\cdot(-1)\cdot2=36+8=44;\ \sqrt\Delta=\sqrt{44}=\sqrt{4\cdot11}=2\sqrt{11}\\\\x_1=\frac{6-2\sqrt{11}}{2\cdot(-1)}=-3+\sqrt{11};\ x_2=\frac{6+2\sqrt{11}}{2\cdot(-1)}=-3-\sqrt{11}\\\\look\ at\ the\ picture\\\\D:x\in\left<-3-\sqrt{11};-3+\sqrt{11}\right>[/tex]
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