The discussion revolves around determining the domains of three functions involving logarithmic and square root expressions. The functions in question are f(x) = ln(1 - ln(x)), g(x) = (x^2 - 1)/(x^4・e^(2x) - 2x^2・e^(2x) - 8e^(2x)), and h(x) = sqrt(6 - e^(-5t)).
The discussion is ongoing, with participants exploring various aspects of the problem. Some guidance has been provided regarding the need to avoid division by zero and the implications of taking square roots of negative numbers. However, there is no explicit consensus on the domains yet.
Participants are working under the assumption that the functions are real-valued, which influences their considerations regarding the domains.
What is the domain of ln(x)? For what x is 1- ln(x) in that set?Kazane said:
You can not divide by 0. Set the denominator equal to 0 and solve for x. Whatever x you get is not in the domain.
You cannot take the sqrt of a negative number (asssuming that these are real valued functions). For what t is 6- e^(5t) negative?