What is the domain of sqrt(x^2-9)?

1 Answer
Lil Del
Oct 11, 2016

The domain of this expression is {x|x < -3 or x > 3}.

Explanation:

To find restrictions to the domain of a square root expression, you must determine which values of the variable will make the radicand have a negative value.

x^2 - 9 < 0
x^2 - 9 + 9 < 0 + 9
x^2 < 9
sqrtx^2 < sqrt9
x < +-3

This actually tells us that x cannot be between -3 and 3, inclusive. Therefore x must be less than -3 or greater than 3.

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