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math question?? is it possible for h(x)= 1/2 [x] to have a domain and range in set notation. if so, can you fi?
is it possible for h(x)= 1/2 [x] to have a domain and range in set notation. if so, can you find it??
1 Answer
- сhееsеr1Lv 71 decade agoFavorite Answer
The function [x] usually denotes the "greatest integer less than or equal to x" -- so the question is when is h(x) defined? Well, any number has such a greatest integer, and the multiplication by 1/2 is fine too.
So the domain is the set:
domain h = { x : x is a real number }
Mathematicians call this set "R" for short.
The range is not. Since [x] produces only integers, h(x) produces only integers or half of integers. You can write this as:
range h(x) = { y : y = n/2 for some integer n }
Mathematicians might write this (1/2) Z because Z denotes the integers.
