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September 3, 2015

Homework Help: domain

Posted by kristie on Monday, July 17, 2006 at 3:22pm.

How do you find the domain of log(x^2-4)?
and how about this one? e^(3x+4)?

Please help me!


Well kristie, you might recognize log(x^2-4) = log((x-2)(x+2)) and then use a property of logs to see it as a sum, i.e., log(ab)=log(a)+log(b). You are then expected to know that the log function is only defined for positve values. Thus you only want x values that make the argument positive.
For the second you want the values that e^y is defined, where y = 3x+4. What values can an exponent be?


thanks, Roger!

I get the first one, but I'm still a little confused about the second one. I thought an exponent could be any values. So would that make (-infinity, _infinity)?


yes, I think you understand it. Exponents can assume any values.
Just beware of a number with a fractional exponent, such as e^(1/(x-1)) for example. Here you need to restrict x not equal 1.

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