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

## Answer This Question

## Related Questions

- Pre-Calc - Does y=1/x have an inverse? It is a one-to-one function, so it should...
- Calc - range of f(x)= 5^(2x^2-1)^(1/2) i know that the domain of the inverse ...
- Calc - Find the inverse of y = ln (x/(x-1))
- Calc - how do you find the inverse of f(x)=6x+10x^17
- inverse - find f^-1 (x). (this is asking me to find the inverse) f(x) = -(x-2)^2...
- calc - How do I find the inverse of a picewise function???
- calc - Find the inverse of each of the following matrices, if possible [i 3 1+i...
- Math- steve? reiny? - 1. Let f(x)=x^5 + 2x^3 + x - 1 Find f^-1(3) and (f^-1)'(3...
- pre-calc - find the inverse of the function f(x) = x^2 − 6x, x ≥ 3
- Math - Find inverse of f if f(x)= x^2-4x+3, (for x is smaller than and equal to ...

More Related Questions