Question

Please Help!!

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = (x-7)/(x+2)
g(x) = (-2x-7)/(x-1)

Answer 1

f(g(x)) =(((-2x-7)-7)/((-2x-7)+2))/(((x-1)-7)/((x-1)+2)))

Answer 2

i already have how to set it up

Answer 3

if you do the algebra right you will have a raft of cancellation and get \(x\)

Answer 4

\[\large f(g(x))=f(\frac{-2x-7}{x-1})=\frac{\frac{-2x-7}{x-1}-7}{\frac{-2x-7}{x-1}+2}\]

Answer 5

clear the complex fraction by multiplying top and bottom by \(x-1\)

Answer 6

you should get
\[\frac{-2x-7-7(x-1)}{-2x-7+2(x-1)}\]

Answer 7

((-2x-7)-7)2((-2x-7)

Answer 8

next step will give \(\frac{-9x}{-9}\)

Answer 9

would that be how i write the numerator?

Answer 10

no it should be what i wrote \[\frac{-2x-7-7(x-1)}{-2x-7+2(x-1)}\]

Answer 11

oh, ok