Assuming the range of #y# is restricted to #RR# (no complex numbers), we know that the expression under the square root must be non-negative. That is,
#(x-a)(x-b)(x-c)>=0#
For #x < a# we get:
#("negative")("negative")("negative")<0# which doesn't meet our condition.
For #a < x < b # we get:
#("positive")("negative")("negative")>0# which meets our condition.
For #b < x < c # we get:
#("positive")("positive")("negative")<0# which doesn't meet our condition.
For #c < x# we get:
#("positive")("positive")("positive")>0# which meets our condition.
Therefore, #x# can be any number in the intervals #[a,b]uu[c,oo)#.
**Note that square brackets are used because if #x# is #a#, #b#, or #c#, then the expression #(x-a)(x-b)(x-c)# is just 0 which is allowed.
