[tex]f(x) = \frac{\sqrt{x^{2}+2x-3}}{\sqrt[3]{x+4}}[/tex]
Licznik:
[tex]\sqrt{x^{2}+2x-3} \geq 0\\\\x^{2}+2x-3 \geq 0\\\\\Delta = b^{2}-4ac = 2^{2}-4\cdot1\cdot(-3) = 4+12 = 16\\\\\sqrt{\Delta} = \sqrt{16} = 4\\\\x_1 = \frac{-2-4}{2} = \frac{-6}{2} = -3\\\\x_2 = \frac{-2+4}{2} = \frac{2}{2} = 1[/tex]
a > 0, to ramiona paraboli są zwrócone do góry
x ∈ (-∞; -3 > ∪ < 1;+∞)
Mianownik:
[tex]\sqrt[3]{x+4} \neq 0\\\\x+4 \neq 0\\\\x \neq -4[/tex]
Łącznie:
x ∈ (-∞;-4) ∪ (-4; -3 > ∪ < 1; +∞)
