Domain of the Function f(x): Explained

[the_storm]

The Question is: What is the Domain of the function f(x)= log_{5}(log_{5}(x + 2)
My answer is that the Domain is (-2, \infty). However the it is said that the right answer is (-1, \infty) and I am not convinced so can anyone give me an explanation?

 

[micromass]

You can't take logs of negative numbers. So you'll need to make sure that

x+2\geq 0

But there's another log in that formula. That log also can't take negatives as input. So moreover, you'll have to make sure that

\log^5(x+2)\geq 0

 

[the_storm]

so Domain is (-1, infinty) right??

 

[micromass]

Yes!

 

[dimitri151]

Just nitpicking to pass the morning. It's not just negative numbers you can't take the log of. It's also zero. You can't take the log of a non-positive number. No?

 

[JCVD]

You cannot take the log of zero.

 

[Landau]

If we are nitpicking: "the domain" of a function is part of the definition of that function. OP is asking for the largest possible domain that is compatible with the given formula.

 

[dimitri151]

It's true Landau, but nobody disputed that.

 

[ayuk]

can you be more explicit