If , then :
is a rational function of
Finding the correct condition:
Given that,
Hence, option A is correct.
We have, , clearly is a rational function of as it is in the form .
Hence, option D is correct.
Explanation for the incorrect options:
Option B:
is not possible as is not defined at .
Hence, option B is incorrect.
Option C: increases with for
Which means decreases with for .
Therefore, option C is incorrect.
Hence, (A), (D) are the correct option.