Question 1125162: The domain of the function
f(x)=sqrt(x^2-13x+36) consists of one or more of the following intervals (-∞,A],[A,B],[B,∞) where A
Find A
Find B
for each interval answer yes or no to shelter the interval is included in the solution.
(-∞,A]
[A,B]
[B,∞)
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The expression is 0 when x = 4 and when x = 9.
So A and B in the problem are 4 and 9.
The graph is an upward opening parabola; so it is positive on (-infinity, 4) and on (9,infinity) and negative on (4,9).
Since the square root of a negative is not real, the domain of the function is where the quadratic expression is 0 or positive.
(-infinity, 4]: yes, part of the domain
(4,9): no, not part of the domain
[9,infinity): yes, part of the domain
A graph, showing that the interval (4,9) is not part of the domain:
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