a) y xác định \( \Leftrightarrow {\rm{ }}{x^2}-{\rm{ }}9{\rm{ }} \ne {\rm{ }}0{\rm{ }} \Leftrightarrow {\rm{ }}x{\rm{ }} \ne {\rm{ }} \pm {\rm{ }}3\)
Vậy tập xác định \(D = \mathbb R\backslash \left\{ { \pm {\rm{ }}3} \right\}\)
b)
y xác định
\( \Leftrightarrow \left\{ \matrix{ 1 - {x^2} \ne 0 \hfill \cr - x \ge 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ x \ne \pm 1 \hfill \cr x \le 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ x \ne - 1 \hfill \cr x \le 0 \hfill \cr} \right.\)
Vậy \(D = (-∞;-1)\cup (-1; 0]\)
c)
y xác định
\( \Leftrightarrow \left\{ \matrix{
2 - x \ge 0 \hfill \cr
x + 2 > 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x \le 2 \hfill \cr
x > - 2 \hfill \cr} \right. \Leftrightarrow - 2 < x \le 2\)
Vậy \(D = (-2, 2]\)
d)
y xác định
\( \Leftrightarrow \left\{ \matrix{ x - 1 \ge 0 \hfill \cr 4 - x \ge 0 \hfill \cr (x - 2)(x - 3) \ne 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ x \ge 1 \hfill \cr x \le 4 \hfill \cr x \ne 2;\,x \ne 3 \hfill \cr} \right. \)
\(\Leftrightarrow \left\{ \matrix{ 1 \le x \le 4 \hfill \cr x \ne 2;x \ne 3 \hfill \cr} \right.\)
Vậy \( D = [1, 2) ∪(2, 3) ∪ (3, 4]\)