The function g is defined by g(x)=(x+1)/(x-2), x is not equal to k and m, find the values of k and m
of course, I know that x is definitely not equal to 2, but how about the other one?
I suspect there is some aspect of this problem being ignored. Is this the exact and complete language of the problem?
$a \in \mathbb R\ and\ a \ne 0 \implies \dfrac{1}{a} \in \mathbb R.$
$\therefore a, b \in \mathbb R\ and\ a \ne 0 \implies b * \dfrac{1}{a} \equiv \dfrac{b}{a} \in \mathbb R.$
So if the only restriction on g(x) is that it is a real-valued function, x = 2 is the only number necessarily outside its domain. Of course the definition of g may exclude any other real number.
Given the answer, I can come up with a question that would have that as its answer. What values of are not in the domain of ? That is the function composed with itself.
From here, you can simplify:
Obviously, for this. But, since is only defined when is defined, we also have .