Find the Domain f(x) = square root of x^2-9
Problem
Solution
Identify the restriction for a square root function, which requires the radicand (the expression inside the root) to be greater than or equal to zero.
Factor the quadratic expression using the difference of squares pattern.
Determine the critical points by setting each factor to zero, which gives
x=3 andx=−3 Test the intervals created by the critical points:
(−∞,−3] [−3,3] and[3,∞)
For
x=−4 (−4)2−9=7≥0 (True)For
x=0 (0)2−9=−9≥0 (False)For
x=4 (4)2−9=7≥0 (True)
Combine the intervals where the inequality holds true to define the domain.
Final Answer
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