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Homework Help: Another inverse problem!

  1. Sep 14, 2003 #1
    i keep getting stuck on these inverse problems...

    the question is

    let f(x)=5+2x+5e^x
    f^-1(10)=?

    i keep messing up on these problems and now im not really sure where exactly 2 start...i know i gotta find the inverse but i would appreciate some help on getting started on this problem.....thx
     
  2. jcsd
  3. Sep 15, 2003 #2

    HallsofIvy

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    There is no way to algebraically find the inverse function to f(x)- not with x both in the exponent and as a base.

    However, the problem does NOT ask you to find "f-1", it only asks you to find "f-1(10)".

    Can you think of a value of x such that f(x)= 10 and what does that have to do with the problem?
     
  4. Sep 15, 2003 #3
    well....f(x)=10 when x=0
    but i dont c ne relation btwn that and the inverse...
     
  5. Sep 15, 2003 #4

    HallsofIvy

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    Then I think we've discovered WHY you keep "getting stuck on these inverse problems"!! That's the DEFINITION of inverse!

    Two functions (call them f and g) are "inverse" to each other (here's the "formal" definition) if and only if f(g(x))= x and g(f(x))= x for all x.

    If f(x)= y, then f-1(f(x))= f-1(y)= x.

    Since f(0)= 10, f-1(10)= 0.

    Whenever f(a)= b, then f-1(b)= a.

    if f: x-> y then f-1y-> x
     
  6. Sep 15, 2003 #5
    thats it?....how come it looks so simple now?....neways thx 4 clearing things up!...
     
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