Найдите область определения функции y=корень четвертой степени из (3x^2+x-4).

\[y = \sqrt[4]{3x^{2} + x - 4}\]

\[3x^{2} + x - 4 \geq 0\]

\[D = 1 + 48 = 49\]

\[x_{1} = \frac{- 1 + 7}{6} = 1;\]

\[x_{2} = \frac{- 1 - 7}{6} = - \frac{8}{6} = - \frac{4}{3};\]

\[3\left( x + 1\frac{1}{3} \right)(x - 1) \geq 0\]

\[x \leq - 1\frac{1}{3};x \geq 1.\]

\[D(y) = \left( - \infty; - 1\frac{1}{3} \right\rbrack \cup \lbrack 1; + \infty).\]