SOLUTION: g(x)= (4/x-1)+1 f(x)=(3/x+2)-1 Are these functions inverses of each other?

Algebra ->  Inverses -> SOLUTION: g(x)= (4/x-1)+1 f(x)=(3/x+2)-1 Are these functions inverses of each other?      Log On


   

Question 996942: g(x)= (4/x-1)+1
f(x)=(3/x+2)-1
Are these functions inverses of each other?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify each of the functions, and then find inverse of either; or once simplified, compose one with the other and solve for the result of that simplified. Is it x? Just do it!

Your functions as you listed:
g%28x%29=+%284%2Fx-1%29%2B1
4%2Fx-1%2B1
highlight_green%284%2Fx%29
f%28x%29=%283%2Fx%2B2%29-1
3%2Fx%2B2-1
highlight_green%283%2Fx%2B1%29
One can judge this far that g and f are NOT inverses of each other.

Try either composition.
g%28f%28x%29%29=4%2F%283%2Fx%2B1%29
4%2F%283%2Fx%2Bx%2Fx%29
4%2F%28%283%2Bx%29%2Fx%29
highlight_green%28%284x%29%2F%283%2Bx%29%29------as simple as can be made. This did not produce the required
result of x.

g and f are not inverses.