Explanation:
To find the nature, position, and size of the image formed by a concave mirror, we can use the mirror formula:

1/f = 1/u + 1/v

where f is the focal length of the mirror, u is the distance of the object from the mirror, and v is the distance of the image from the mirror.

Step 1: Determine the values of f and u.

Given f = 4cm and u = 9cm.

Step 2: Calculate v using the mirror formula.

1/4 = 1/9 + 1/v

Multiplying both sides by 36v, we get:

9v = 4v + 16

5v = 16

v = 3.2cm

Therefore, the image is formed 3.2cm away from the mirror.

Step 3: Determine the nature of the image.

Since the object is placed beyond the focal point of the mirror, it is a real object. When a real object is placed in front of a concave mirror, the image formed can be either real or virtual, depending on the position of the object. In this case, the image is formed between the focal point and the mirror, so it is a real image.

Step 4: Calculate the size of the image.

To calculate the size of the image, we can use the magnification formula:

m = -v/u

where m is the magnification of the image.

m = -3.2/9

m = -0.36

Since the magnification is negative, the image is inverted.

The size of the image can be calculated using the formula:

h' = -m*h

where h is the height of the object and h' is the height of the image.

h' = -(-0.36)*2

h' = 0.72cm

Therefore, the size of the image is 0.72cm.

Conclusion:
The image is a real and inverted image formed 3.2cm away from the mirror with a size of 0.72cm.