Choose the correct mirror image of fig(x), when mirror is placed at the right side.

The correct option is (2).

Understanding Mirror Images:
When a vertical mirror is placed to the right of a figure, the resulting mirror image undergoes a lateral inversion. This means:
1. The left and right sides of the figure are interchanged (elements on the left side move to the right side, and vice versa).
2. The top and bottom orientations remain unchanged (there is no vertical inversion).
3. The shading or division within individual elements also undergoes lateral inversion (left-shaded portions become right-shaded, and vice versa).

Let us analyze each element of Fig(x) step-by-step to find its mirror image:

1. The Small Circle:
- In Fig(x), the small circle is located on the upper-left boundary of the large triangle, and its right half is shaded black.
- In the mirror image, the circle must move to the upper-right boundary of the large triangle, and its left half must be shaded black.
- Looking at the options, only Option (2) correctly shows the circle on the right side with its left half shaded black.

2. The Vertical Arrow:
- In Fig(x), the arrow is in the lower-left section, with its left side shaded black.
- In the mirror image, the arrow must be in the lower-right section, and its right side must be shaded black.
- Option (2) correctly displays this inverted arrow placement and shading.

3. The Small Triangle:
- In Fig(x), the small triangle is in the lower-right section, with its bottom-left corner shaded black.
- In the mirror image, this small triangle must appear in the lower-left section, and its bottom-right corner must be shaded black.
- Option (2) matches this configuration perfectly.

By combining all these observations, we find that only Option (2) satisfies all the conditions of lateral inversion.