`f(x) = |x + 2|, [-2, oo)` Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

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embizze eNotes educator| Certified Educator

We are asked to show that `f(x)=|x+2|,[-2,oo) ` has an inverse by showing that the function is monotonic on the interval using the derivative:

By definition, ` f(x)=|x+2|={[x+2,x+2 >=0],[-x-2,x+2<0]}`

x+2>0 ==> x>-2 which is the interval we wish so on the interval f(x)=x+2.

f'(x)=1 which is positive for all x in the interval so the function is monotonic (strictly increasing) on the interval. Thus the function has an inverse.

The graph: