What's the domain of log(x-2) + log(x+2)? It's x > 2.Can someone please explain why these two functions have different domains when to me they are the same function?
1. f(x)= log(x-2) + log (x+2)
2. f(x)= log(x^2-4)
If I simplify 1. I get 2. and therefore the domains should be the same?
Can someone please explain why these two functions have different domains when to me they are the same function?
1. f(x)= log(x-2) + log (x+2)
2. f(x)= log(x^2-4)
If I simplify 1. I get 2. and therefore the domains should be the same?
What's happening here is that simplifying (or, more generally, rewriting using properties of the log) can change the domain, so that the result is technically a different function.Can someone please explain why these two functions have different domains when to me they are the same function?
1. f(x)= log(x-2) + log (x+2)
2. f(x)= log(x^2-4)
If I simplify 1. I get 2. and therefore the domains should be the same?
Strictly speaking, the functions are not equivalentWhat to me are equivalent functions not having the same domain still confuses me.
Here is what is going on--basically what Dr Peterson said.I appreciate what you are all saying but I still find this a bit weird. What to me are equivalent functions not having the same domain still confuses me.
Thanks for your help. I’ll consider your replies for a while and hopefully a light bulb will come on at some stage.
What is log(-4) + log(-4)? It doesn't exist. But log(-4) + log(-4) = log(16), which does exist.