# Bayesian Likelihood function range

I have given a prior which has a range of data between[0.5,1.5] and a normal distribution N(0.9,1) which should truncate at the above range and normalize.

also I have the likelihood distribution in a form of errors distributed normally N(0,1)

when I try to write the likelihood function should I take the range [0.5,1.5] itself? or I should take the range from [0,inf]?