Determine the natural domain of
Answer & Explanation
For the square root to yield real numbers it must hold that
Now consider the denominator. First of all, the natural logarithm must take in positive values of x, so . Besides that, the denominator cannot be 0. The logarithm assumes that value at
Now what you do is the intersection of all of these constraints to obtain your domain.
If N is such that the square root stays below 1, the set substraction operation will just yield the interval
Most Popular Questions