Posted by Brandon on .
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)
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.