Question

g^-1:x = 5 / x-3
find
a---the function of g(x)
b---object of g(x) if the image is 2

Answer 1

for the first one, solve
\[x=\frac{5}{y-3}\] for \(y\)
can you do that?

Answer 2

one way is to take the reciprocal of both sides and get
\[\frac{1}{x}=\frac{y-3}{5}\] then
\[\frac{5}{x}=y-3\] and so
\[y=\frac{5}{x}+3\] there is another way too
in case
\[g:x\to \frac{5}{x}+3\]

Answer 3

how about b?

Answer 4

strange wording to me, but i think it means
"if \(g(x)=2\) then what is \(x\)?" and the answer is
\(g^{-1}(2)=\frac{5}{2-3}=\frac{5}{-1}=-5\)

Answer 5

that is the point of the inverse function. it tells you what input you used to get an output

Answer 6

another way of viewing this is elementary algebra
\[\frac{5}{x}+3=2\] solve for \(x\)