How to computer f^1(x) using limit definition
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How to computer f^1(x) using limit definition

[From: ] [author: ] [Date: 11-06-28] [Hit: ]
I dont understand how to do this when it does give you the x.... Thanks for the help!_________________________________-Can you rephrase that question,......
For example, f(x)=x^2+x.... I don't understand how to do this when it does give you the x.... Thanks for the help!

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     f(x) = x² + x
f(x+h) = (x+h)² + (x+h) = x²+2hx+h² + x+h


                     f(x+h) - f(x)
f '(x) = lim ———————
          h→0          h



                     (x²+2hx+h² + x+h) - (x² + x)
f '(x) = lim ——————————————
          h→0                       h


                     x²+2hx+h² + x+h - x² - x
       = lim ——————————————
          h→0                       h


                          2hx+h²+h
       = lim ————————
          h→0              h


                         h(2x+h+1)
       = lim ————————
          h→0              h



       = lim (2x+h+1)  =  2x+0+1  =  2x + 1            ← ANSWER
          h→0



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Can you rephrase that question, or explain what you're really trying to do, at least with the f^1(x) part?
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