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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