Question

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

`f(x)= (x-9)/(x+5)`

`g(x)= (-5x-9)/(x-1)`

`f(g(x))= ( (-5x-9)/(x-1) -9)/( (-5x-9)/(x-1)+5 )`

`f(g(x))= (-5x-9-9(x-1))/(-5x-9+5(x-1))`

`f(g(x))= (-5x-9-9x+9)/(-5x-9+5x-5)`

`f(g(x))= (-14x)/(-14)=x`

`g(f(x))= (-5 (x-9)/(x+5)-9 )/( (x-9)/(x+5)-1 )`

`g(f(x))= (-5x+45-9(x+5))/(x-9-1(x+5))`

`g(f(x))= (-5x+45-9x-45)/(x-9-x-5)`

`g(f(x))= (-14x)/(-14)=x`