f(f(x)) when f(x)=sqrt(x^2-5^2) and what is its domain?

Answer 1

If x is less than 5, then x^2-25 will be negative and you can't have the square-root of a negative number, now can you? (At least not in the real number world -- I will assume you aren't yet working with imaginary numbers).

So, x >= 5, BUT x can also be negative because the square of a negative number is positive, so any number less than or equal to -5 will be OK, too.

-5 <= x >= 5 is the domain. You can also write it as: |x| >= 5

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