Question

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 and
g(x) = -2x-7 / x-1

Answer 1

Please help :)
I forgot how to do this but you should have covered it already.

Answer 2

yes i did :) hold on

Answer 3

Oh yay you're typing i'm still here

Answer 4

its gonn start like tht

Answer 5

I did get that far. My big question is after this step and how to take it. Do I flip the denominator and multiply both terms?

Answer 6

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

Answer 7

what @kiimiilee wrote is correct
here is the first step :

Answer 8

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

Answer 9

Does x=-7/2?

Answer 10

from there on in it is a bunch of annoying algebra, which will lead to a whole raft of cancellation, and you should end up only with \(x\) at the end

Answer 11

no, \(x\) is not a number at all
your job is to compose the function and find that you end up with the identity, i.e. that
\[f(g(x))=x\]

Answer 12

So if I demonstrate that both f(g(x)) and g(f(x)) = -7/2 would I be answering the questioN?

Answer 13

yes but it would be wrong

Answer 14

Ok then where would I go from there.

Answer 15

you simplify i think @satellite73

Answer 16

multiply top and bottom by x-1

Answer 17

OK then what?

Answer 18

you keep canceling and you'll get x

Answer 19

ok ty

Answer 20

np :)