SOLUTION: I need to show that f(x)=(3-x)/(x) and f^(-1)(x)=(3)/(x+1) are inverses.

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Question 762468: I need to show that f(x)=(3-x)/(x) and f^(-1)(x)=(3)/(x+1) are inverses.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Inverse, means one undoes the other.

If y=f(x), then f(x) = y

Assume there is also a function g(x).
If g(x) is input for f(x), OR if f(x) is input for g(x), and if g(f(x))=x and f(g(x))=x, then g(x) is the inverse function of f(x). See, one function undoes the other. You can also say, f(x) and f^(-1)(x) are inverses.

Now you ask if f%28x%29=%283-x%29%2F%28x%29 and f%5E%28-1%29%28x%29=%283%29%2F%28x%2B1%29 are inverses.
Just use the idea of one of them being inverse of the other.
Fill this form: f%28f%5E%28-1%29%29=%283-%28f%5E%28-1%29%28x%29%29%29%2F%28f%5E%28-1%29%28x%29%29
f%28f%5E%28-1%29%29=%283-%283%2F%28x%2B1%29%29%29%2F%283%2F%28x%2B1%29%29=?

If the result is x, then these two function ARE inverses.
(Actually, you also need to check f(x) as input for the f^(-1) also to be certain).