Functions

To determine the interval where the function is strictly decreasing, we need to find the derivative and analyze its sign.
First, compute the derivative:

.
The derivative is:

.
Set to find where the function is strictly decreasing:

.
Multiply through by to clear the fraction:

.
Multiply by to further simplify:

.
Rearrange to:

.
Solve for :

.
However, since (as is undefined at ), the final interval where is strictly decreasing is:
.

To solve this type of matching problem, we analyze each function from List-I and determine where it is increasing. Let's go through each one:

(A)

To find where is increasing, we can take its derivative and determine where it is positive. The derivative is:

Set :

The function is increasing in .

(B)

Taking the derivative:

Set :

The function is increasing in .

(C)

Taking the derivative using the logarithm derivative rule:

Set :

The function is increasing in .

(D)

Taking the derivative:

Set :

Use the range expression: , so

The function is increasing in .

Matching Results:

Comparing these intervals with List-II:

Therefore, the correct answer is: (A-IV), (B-I), (C-III), (D-II)