confirm that f and g are inverses by showing that f(g(x))= x and g(f(x))?

Question

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

explain to me how you work this out.
thanks.

i got this out of my pre calculus book.
=)

Answer 1

simple, plug one equation into the other, so for f(g(x)) = x, wherever you see x in the f(x) = x + 1/x equation, simply plug in (1/x -1) then solve. basically, to prove f(g(x)) = x, solve this equation:

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

do the same substitution for g(f(x)) and if they are both inverses of each other then both equations should work out.

Answer 2

What math are you in? I'm in calculus. Is this something you found on a test? Well, anyway, f(g(x)) would be f(1/x-1), and g(f(x)) would be g(x+1/x). So, FOIL (x+1/x(1/x-1)), also known as (x+1/x)(1/x-1) (this should make things a little more clear, and you will get x-x+1/(x^2)-1/x. So, I agree, I don't think that they are inverse functions. There's a problem with the assignment, and if you get marked off for it, you should complain. That's what I would do.

Answer 3

I think you wrote the question incorrectly. It should be
f(x) = (x+1)/x and g(x) = 1/(x-1)...paranthesis change everything.

f(g(x))=f(1/(x-1)) = ((1/(x-1))+1) / (1/(x-1))
this simplifies to ((1+x-1)/(x-1))/(1/(x-1)), which further reduces to:
(x/(x-1))/(1/(x-1)), the (x-1) cancel each other out leaving just x. Do the same process works for g(f(x))....this ones simpler