Question

hi-- G(w)= 3+2/w-1. is G(w) = -1 in range? I think it should be, but to find the domain I plug in -1 and am getting w=-1. The book gets 1/2.

Answer 1

I assume you mean to have parentheses like
G(w)=3+2/(w-1)
correct?

Answer 2

\[G(w)=3+2/(w-1)\]?????????????

Answer 3

yes :)

Answer 4

any thoughts?

Answer 5

ok so if -1 is in the range we must find some w such that
G(w)=-1=3+2/(w-1)
-4=2/(w-1)
w-1=-1/2
w=1/2
so there is the answer.
You say "to find the domain I plug in -1 and am getting w=-1"
which is not right, you seem confused.
The Domain is the set of all w for which G(w) is defined, so the Domain is
\[w \neq 1\]because when w=1 we get\[G(w)=3+2/0=undefined\]The Range are all possible values of the function G(w).