I was *interested in:
A Procedure for finding the domain of $\color{green}{\text{algebraically combined functions}}$ and $\color{green}{\text{algebraically combined functions}}.$
Assignment Questions [already Submitted]
Given
- $f(x)=\sqrt{1-2x}$
- $g(x)=\frac{x}{x^2-1}$
Find the domain of
- $\Large\frac fg$
My Answer
$(-\infty, 1) \;\cup\;(-1,0) \;\cup\;(0,\frac12]$
- $\large gf^2$
My Answer
$(-\infty, -1) \;\cup\;(-1,\frac12]$
I was told that answers are incorrect, but from my understanding the domain of algebraically combined functions is the intersection of the functions domain. Is it?
If someone could help clear up my confusion, that would be great. And, if possible, any clear, procedural methods for finding the domain of a composition of functions and algebraically combined functions or, better yet, a link/suggested reading that is clear and intuitive for finding the domain.