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:
=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:
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