For the mapping
the image of [ 1 , 2 ] {\displaystyle {}[1,2]} is the set of all squares of real numbers between 1 {\displaystyle {}1} and 2 {\displaystyle {}2} , this is thus [ 1 , 4 ] {\displaystyle {}[1,4]} . The preimage of [ 1 , 4 ] {\displaystyle {}[1,4]} consists of all real numbers whose square is between 1 {\displaystyle {}1} and 4 {\displaystyle {}4} . This is [ − 2 , − 1 ] ∪ [ 1 , 2 ] {\displaystyle {}[-2,-1]\cup [1,2]} .
![{\displaystyle {}[1,2]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d41d1e45b84d775d096bafb9710b0746d7df1b3f)
is the set of all squares of real numbers between
and 
,
this is thus ![{\displaystyle {}[1,4]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e1aa329024219cda380773d0f4815acce3e3ccf5)
. The preimage of consists of all real numbers whose square is between
and 
.
This is ![{\displaystyle {}[-2,-1]\cup [1,2]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69de43d35bfc285ac459e3518902a13aa8d9bd68)
.
