a) Ta có:
y xác định khi và khi chỉ khi:
\(\eqalign{
& \log ({x^2} - 5x + 16) < 1 \Leftrightarrow 0 < {x^2} - 5x + 16 < 10 \cr
& \Leftrightarrow \left\{ \matrix{
{x^2} - 5x + 16 > 0 \hfill \cr
{x^2} - 5x + 6 < 0 \hfill \cr} \right. \Leftrightarrow 2 < x < 3 \cr} \)
Vậy D = (2, 3)
b) Ta có:
y xác định khi và chỉ khi:
\(\eqalign{
& \left\{ \matrix{
{\log _0}_{,5}( - {x^2} + x + 6) \ge 0 \hfill \cr
{x^2} + 2x \ne 0 \hfill \cr} \right. \cr&\Leftrightarrow \left\{ \matrix{
0 < - {x^2} + x + 6 \le 1 \hfill \cr
x(x + 2) \ne 0 \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
{x^2} - x - 6 < 0 \hfill \cr
{x^2} - x - 5 \ge 0 \hfill \cr
x \ne 0;\,\,x \ne - 2 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
- 2 < x < 3 \hfill \cr
\left[ \matrix{
x \le {{1 - \sqrt {21} } \over 2} \hfill \cr
x \ge {{1 + \sqrt {21} } \over 2} \hfill \cr} \right. \hfill \cr x \ne 0;\,\,x \ne - 2 \hfill \cr} \right.\cr& \Leftrightarrow \left\{ \matrix{
- 2 < x \le {{1 - \sqrt {21} } \over 2} \hfill \cr
{{1 + \sqrt {21} } \over 2} \le x < 3 \hfill \cr} \right. \cr} \)
Vậy \(D = ( - 2;\,{{1 - \sqrt {21} } \over 2}{\rm{]}} \cup {\rm{[}}{{1 + \sqrt {21} } \over 2};\,3)\)
