Question

.Найти область определения функции.$y= sqrt{3x+4- x^{2} }$ .

Answer 1

y=√(3x+4-x²);⇒
3x+4-x²≥0;⇒
x²-3x-4≤0;
x²-3x-4=0;⇒x₁,₂=3/2⁺₋√(9/4+4)=3/2⁺₋√25/4=3/2⁺₋5/2;
x₁=3/2+5/2=8/2=4;
x₂=3/2-5/2=-2/2=-1;
-1≤x≤4;