I found an example of inverse homomorphism of regular expression (00+1)* (on page no 131 of 'Hopcroft, Motwani, ullman' book).
If h(a)=01 and h(b)=10 then auther says that inverse homomorphism of the given regular expression is regular expression (ba)*.
But there are strings 00 and 1 in the language of (00+1)* which cannot be represented by any string in language of (ba)*.
Is this example wrong or Am I thinking in wrong direction?
It is not strings in the language (ba)* that represent strings in (00+1)* but the other way round. The homomorpisam maps from the alphabet of (ba)* to strings over the alphabet of (00+1)*. Therefore the INVERSE homomorphism maps the other way round.
The image contains all strings that have a picture in (00+1)* . As you observe correctly, 00 and 1 do not have pictures. Therefore they do not contribute anything. This is how inverse morphisms are different from non-inverse ones. The decisive fact is that all the strings that do contribute, contribute strings from (ba)*.