Use the mirror equation to deduce that :
b) a convex mirror always produces a virtual image independent of the location of the object.
[Note : The exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

Explanation

The mirror equation is `(1)/(u)+(1)/(v)=(1)/(f)`
But `m=(upsilon)/(u)=(f)/(u-f)=(upsilon-f)/(f)`
Hence `m=(f)/(u-f)`
`upsilon =f(m+1)`
b) For mirror formula,
`upsilon =(uf)/(u-f)`
Since for a convex mirror, fis positive and u is always negative, `upsilon` will be always positive image and will be formed behind the mirror and will be virtual.