Question 519992: Hi! I'm working on this problem. Find the domain and range of f(x)=ln((x^2)-9)
I've worked out that the domain, in interval notation, is (-∞,-3) U (3,∞) which I'm pretty sure is correct. However, I can't work out what the range should be in interval notation because of the infinities. Any help would be appreciated!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I've worked out that the domain, in interval notation, is (-∞,-3) U (3,∞) which I'm pretty sure is correct. However, I can't work out what the range should be in interval notation because of the infinities. Any help would be appreciated!
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You got the domain correct.
As for the range, you will notice in the interval 0 < x < 1, that is, x is a fraction or decimal, as x approaches but never reaches zero, log x will become increasingly negative. For example, log(.0001)=-4, and log(.000001)=-6. For interval x>1, I think it is easy to see that log x will approach ∞.
So it seems the range for the log function is (-∞,∞)
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