Find the inverse of f(x) = (x+2)/x
To find an inverse, follow the three step process,
1. Rerite the function from y=f(x) as x=f(y).
2. Solve for y in terms of x, if possible.
3. Verify that f(f-1(x))=x
1. y = (x+2)/x becomes x=(y+2)/y
2. Solve for y in terms of x:
xy=y+2
y(x-1)=2
y=2/(x-1)
3. Calculate
f(f-1(x))
= f(2/(x-1))
=2/(x-1)+2)/(2/(x-1))
=x, therefore inverse is correct
The inverse exists only if the function is one-to-one and onto on the domain.
See illustration and note that the function is one-to-one on its domain, and that the inverse intersects the function at x=y:
http://img574.imageshack.us/img574/5812/1291623706.png