Question

Help please, will give medal. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = (x-9) / (x+5) and g(x) = (-5x-9)/(x-1).

Answer 1

you need to simplify \(f(g(x)) = \frac{\frac{-5x-9}{x-1}-9}{\frac{-5x-9}{x-1}+5}\)

Answer 2

any idea where to start?

Answer 3

hint: first simplify \[\frac{-5x-9}{x-1}-9\]

Answer 4

then simplify the bottom.

Answer 5

would i multiply -9 by x-1 to get it off the bottom?

Answer 6

so -5x-9 -9x +9

Answer 7

@zzr0ck3r so i got that first part simplified, f(g(x)) or whatever. how would i set up g(f())

Answer 8

(x))

Answer 9

\[ \large
f(g(x)) = \frac{\frac{-5x-9}{x-1}-9}{\frac{-5x-9}{x-1}+5} =
\frac{-5x-9-9x+9}{-5x-9+5x-5} = \frac{-14x}{-14} = x \\ \large
\text{ } \\ \Large
\text{ } \\ \Large

g(f(x)) = \frac{-5\{\frac{x-9}{x+5}\}-9}{\{\frac{x-9}{x+5}\}-1} =
\frac{-5x+45-9x-45}{x-9-x-5} = \frac{-14x}{-14} = x
\]