How to solve below question?

Suppose we apply the following operations to input image f:

a. 1x3 mean filter (centered about origin) applied to f to give output f1.

b. 3x1 mean filter (centered about origin) applied to f to give output f2.

c. Take the mean (average) of f1 and f2 to get the final output.

These three operations can be done all at once with one mask operator. Derive this operator, carefully specifying the origin and mask weights. You must justify your answer.