One sided limits question

g(r) = 2r + 3 if r < 1
= 2 if r - 1
= 7 - 2r if 1 < r

a. limit of g(r) as r --> 1+
b. limit of g(r) as r --> 1-
c. limit of g(r) as r -->1

as r --> 1+ then g=7-2r then g-->7-2(1)=5

as r --> 1- then g=2r+3 then g-->2(1)+3=5

since for both r --> 1+ and r --> 1- then g--->5 then for r --> 1 then g--->5 too. If the values were different for left and right hand side, g at 1 had no definite limit.