An image is 4.0 cm behind a concave mirror with a focal length of 5.0 cm. Where is the object?
Solve the thin lens equation (which also applies to mirrors):
1/f = 1/r1 + 1/r2 (where r1 is the object distance and r2 is the image distance)
1/r1 = 1/f – 1/r2
r1 = 1/(1/f – 1/r2)
For a concave mirror f is positive, and with the image behind the mirror, the image distance r2 is negative, so
r1 = 1/(1/0.05 – 1/-0.04) = 1/45 = 0.02222 m, answer D.
On the plus side, it puts the object in front of the mirror, which is lucky because you can’t have the object behind the mirror!
EDIT: I rewrote the entire answer because I misread the question as regarding a concave lens, not a mirror.