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Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

f(x) = abs. val. (x + 2), [-2, infinity)

  • Calc -

    Please do not change screen-names. It is easier for Erica/Brandon because reference can be made to a previous problem.

    For this problem, you do not need to find f'(x), because it consists of two straight lines that intersect. A single straight line is monotonic if it is not horizontal.

    Treat f(x) as two separate parts:
    f(x)=-(x+2) if x<-2, and
    f(x)=x+2 if x≥-2.

    So if the domain is given in [2,∞], it consists of a straight line and therefore has an inverse.

    Follow the steps set out in your previous question to find the inverse, if necessary, or as practice.

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