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Question 398046: What is the domain of the function: sqrt(x(x-7)). Write the answer in interval notation.
Answer by dnanos(83)   (Show Source):
You can put this solution on YOUR website! x(x-7) must have positive values, or zero, in order the square root of it to be a real number.
That happens in the following cases:
(i) x>=0 and x-7>=0
(ii) x<=0 and x-7<=0
The zeros of x(x-7) are 0 and 7
the conditions (i) is valid when x>=7
the condition (ii) is valid if x<=0
--------------0------7---------------
+ ~~~~~~~~~~~ - ~~~~~~~~~~ +
So the intervals for sqr[x(x-7)] to be a real number are (-∞ ,0] and [7,+∞)
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