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Find the natural domain of y=1/sqr(-(2-x))
Thanks!
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The natural domain is the set of solutions of this inequality
-(2-x) >= 0, (1)
making an expression under the square root positive (non-negative, to be precise).
The inequality (1) is equivalent to
2-x <= 0 ( ! notice I changed signs in both sides, and changed the inequality sign to the opposite ! )
2 <= x, or, which is the same,
x > = 2.
Answer. The natural domain is the set {x | x >= 2}.
For example, x= 3 is in the domain, while x = 1 is not.