Odpowiedź:
[tex]zad.1~~3x-1\geq 0~~\Leftrightarrow ~~x\in < \dfrac{1}{3},+\infty )[/tex]
[tex]zad.2~~4-x^{2} > 0~~\Leftrightarrow~~x\in (-2,2)[/tex]
Szczegółowe wyjaśnienie:
[tex]zad.1\\\\3x-1\geq 0~~\mid +1\\\\3x-1+1\geq 1\\\\3x\geq 1~~\mid \div 3\\\\x\geq \dfrac{1}{3}\\ \\x\in < \dfrac{1}{3},+\infty )\\\\Odp:~~3x-1\geq 0~~\Leftrightarrow ~~x\in < \dfrac{1}{3},+\infty ).[/tex]
[tex]zad.2\\\\4-x^{2} > 0\\\\a=-1~~\Rightarrow~~ramiona~~paraboli ~~skierowane~~w~~dol\\\\korzystam~~ze~~wzoru~~skroconego~~mnozenia:~~x^{2} -y^{2} =(x-y)\cdot (x+y)\\\\2^{2} -x^{2} > 0\\\\(2-x)\cdot (2+x) > 0\\\\2-x=0~~\lor~~2+x=0\\\\x=2~~\lor~~x=-2\\\\4-x^{2} > 0~~\Leftrightarrow~~x\in (-2,2)\\\\Odp:~~4-x^{2} > 0~~\Leftrightarrow~~x\in (-2,2)[/tex]
