Calc
posted by Erica on .
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(x1)=2
y=2/(x1)
3. Calculate
f(f^{1}(x))
= f(2/(x1))
=2/(x1)+2)/(2/(x1))
=x, therefore inverse is correct
The inverse exists only if the function is onetoone and onto on the domain.
See illustration and note that the function is onetoone on its domain, and that the inverse intersects the function at x=y:
http://img574.imageshack.us/img574/5812/1291623706.png