# Calc

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

• Calc -

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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