Question 1133768
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For the square root of an expression to be a real number, the expression has to be zero or positive.<br>
In this example, the expression under the radical is (x-a)(x-b)(x-c), and we are given the condition that a < b < c.<br>
That expression has the value 0 when x is a, b, or c; so the values a, b, and c are all in the domain.<br>
For the intervals into which the rest of the number line is divided by those three values...<br>
if x > c, then all three factors in the expression are positive, so the product is positive;
if b < x < c, then the factor (x-c) is negative, so the product is negative;
if a < x < b, then the factors (x-b) and (x-c) are both negative, so the product is positive; and
if x < a, then all three factors are negative, so the product is negative.<br>
Now you should be able to determine the domain....