Asked by Brandon
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)
f(x) = abs. val. (x + 2), [-2, infinity)
Answers
Answered by
MathMate
Please do not change screen-names. It is easier for Erica/Brandon because reference can be made to a previous problem.
http://www.jiskha.com/display.cgi?id=1291619172
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.
http://www.jiskha.com/display.cgi?id=1291623706
http://www.jiskha.com/display.cgi?id=1291619172
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.
http://www.jiskha.com/display.cgi?id=1291623706
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.