How do you know when to use brackets or parenthesis in finding domain or range?

Question

Eli Assouline · Accepted Answer

Please see below.

Use a bracket (sometimes called a square bracket) to indicate that the endpoint is included in the interval, a parenthesis (sometimes called a round bracket) to indicate that it is not. Brackets are like inequalities that say "or equal" parentheses are like strict inequalities. #(3,7)# includes #3.1# and #3.007# and #3.00000000002#, but it does not include #3#. It also includes numbers greater than #3# and less than #7#, but it does not include 7. People sometimes say this is #3# to #7# "exclusive" (Excluding the endpoints) #[4, 9]# includes #4# and every number from #4# up to #9#, and it also includes #9# People sometimes say this is #4# to #9# "inclusive" (Including the endpoints) #(a,b) = {x : a< x " and " x< b}# #[a,b] = {x : a<= x " and " x<= b}# Of course, mixed intervals #(a,b]# or #[a,b)# are also possible. The symbols #-oo# (and #oo#) are used to indicate that there is no left (right) endpoint for the interval. They are not endpoints, but indicators that there is no endpoint. They always take parentheses. Quick examples: Domain of #f(x)=sqrtx# is #[0, oo)# #" "# #(sqrt0 = 0# is a number.) Domain of #g(x)=1/sqrtx# is #(0, oo)# #" "# #(1/sqrt0# is a not number.)

Savannah Anderson · Answer

undefined Parentheses () are typically used when indicating open intervals, where the endpoints are not included in the set. Brackets [] are used when indicating closed intervals, where the endpoints are included in the set. When finding the domain or range of a function, you use parentheses for values that are not included in the set and brackets for values that are included.