Expand
This gives . Now you can get all your x terms on the LHS and factor
What is the inverse of f(x) = x/x-1 ?
this is my attempt to solve it:
y = x / x-1
y(x-1) = x
hence x(x-1) is the inverse.....
however, substituting with x=5 gives......
5/4=1.25
so pluging this is the inverse function should give 5, right?
lets see:
1.25(1.25-1) = 1.25*.25= 0.3125. WRONG!!
can anyone tell me where I went wrong?
thanks
Two comments.
1. Another way to find the inverse function is to switch the roles of x and y. For example:
Now solve for y and you get your inverse function.
2. Please be more careful in how you write you problem. For example:
is really
What you meant to write is y = x/(x - 1). Please use parentheses in the future.
-Dan
To expand on this, functions that are their own inverses are called involutes. It is simple to show that the following functions are involutes:
f(x) = x.
f(x) = -x + b, where b is a real number.
where a, b and c are real numbers. f(x) = 1/x is included as a special case.
The question I'll pose for the interested reader is: Are the above functions the only involutes?