Given:
The range of a function is .
To find:
The function for the given range from the given options.
Solution:
In option A, the given function is:
Here, is always greater than 0. So, is also greater than 0, i.e., .
In option B, the given function is:
Here, is always greater than 0. So, is also greater than 0, i.e., .
In option C, the given function is:
Here,
The range of this function is . So, option C is correct.
In option D, the given function is:
Here,
The range of this function is
Therefore, the correct option is only C.