Задача 1392

Найти область определения для следующих функций:

a) $\displaystyle a(x) = \frac{x^{3} + 5x}{x^{2} + 4x + 4}$
\hfill b) $\displaystyle b(x) = \frac{2 - x}{x^{2} - 10x + 21}$
\hfill c) $\displaystyle c(x) = \frac{5x + 37}{x^{2} + 3}$

d) $\displaystyle d(x) = \frac{3x + 4}{x - 10}$
\hfill e) $\displaystyle e(x) = \frac{x^{3} - 4x^{2} + 5x - 7}{x^{2} - 4}$
\hfill f) $\displaystyle f(x) = \frac{1}{\sqrt{x^{2} - 5x + 6}}$

g) $\displaystyle g(x) = \sqrt{x^{2} - 5x + 4}$
\hfill h) $\displaystyle h(x) = \sqrt{8x - 20}$
\hfill i) $\displaystyle i(x) = \sqrt{6 + x + x^{2}}$

j) $\displaystyle j(x) = \sqrt{\frac{(4 - x)(x^{2} + 1)}{(x - 3)^{2}}}$
\hfill k) $\displaystyle k(x) = \frac{1}{\sqrt{x^{2} + x - 20}}$

l) $l(x) = \displaystyle \sqrt{\frac{\sqrt{17 - 15x - 2x^{2}}}{x + 3}} + \frac{x + 3}{\sqrt{(x + 2)^{2}}}$
\hfill m) $m(x) = \displaystyle \frac{x + 1}{(9 - x^{2})\cdot\sqrt{-2x^{2} - 11x + 13}}$

n) $\displaystyle n(x) = \frac{\sqrt{x + 1001}}{\sqrt{30 - x - x^{2}}}$
\hfill o) $\displaystyle o(x) = \frac{5}{\sqrt{x^{2} + 3x - 10}} + \frac{8}{2x - 7}$
\hfill p) $p(x) = \sqrt{30 + x - x^{2}}$