Posted by **Erica** on Monday, December 6, 2010 at 3:21am.

Find the inverse of f(x) = (x+2)/x

- Calc -
**MathMate**, Monday, December 6, 2010 at 7:58am
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

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