Domain of f(x)?
#f(x)=sqrt(x^2-2)/sqrt(x^2-9)#
2 Answers
graph{sqrt(x^2-2)/sqrt(x^2-9) [-10, 10, -5, 5]}
The domain in interval notation is -
Explanation:
Solve this by checking which values make the function undefined. Under the square root, nothing can be negative. In the denominator, nothing can be zero. If x=3, the denominator becomes 0, so x must be bigger than 3. However anything smaller than -3 also works, since x is squared. So, the function is undefined between -3 and 3, and defined everywhere else, making the domain
Note that in both 3 and -3 are not included, since the function is defined at both those values.
The domain must prevent the arguments of the square roots from becoming negative:
Also the denominator must not become 0, therefore, the second equation must not allow equality:
Logically, the above becomes
Because of the way that the square root works, we obtain two regions:
The above is the domain.