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How would you interpret "for each of the intervals I, give the domain and range of the restriction $f_{I}$ of $f$ to I and sketch the graph of the inverse of $f_{I}$ "?

The intervals are (∞,0], [0,2] and [2,∞) and the equation of the function is $f(x)=x^3-3x^2+4$.

randb
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1 Answers1

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It means you have three intervals, and you have to do the same thing for each of the intervals:

  1. You have to give the domain of $f_{(-\infty, 0]}$
  2. You have to give the range of $f_{(-\infty, 0]}$
  3. You have to sketch the graph of the inverse of $f_{(-\infty, 0]}$

Then you have to repeat the three steps two more times. Now, which of the three steps is confusing you?

5xum
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  • How do I go about finding the inverse of the cubic? – randb Apr 05 '17 at 08:38
  • @randb Well the question only says "sketch a graph". So you don't have to probably. Just draw the graph of $f$ and mirror it across the line $y=x$... – 5xum Apr 05 '17 at 08:40