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Because x in the rule is square root on the right hand side I can understand why only a positive number would be allowed in the left hand side value of x.

I undertand that because x cannot be less than 0, but the square root of x can be any positive number, then the interval notation I understand would be [0, infinity)

zero because x cannot be less than 0, and infinity because x can be any other number.

OK, this is where I have a problem understanding.

h(x) = 1/x

x cannot be zero, the function h has domain R excluding 0, I am to understand this consists of two open intervals.

I understand that x can be any negative number, but am failing to understand why 0 is then included, the interval is written as ( - infinity, 0)

I am told that R excludes 0, so then how can the open interval include (0, infinity).

I understand the infinity part, but x cannot be zero so where does that arrive in the interval?

Please advise if you can.