1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inverse and composition of functions

  1. Nov 10, 2015 #1
    1. The problem statement, all variables and given/known data

    If ##f(2x-1)= 6x + 15## and ##g(3x+1)=\frac{2x-1}{3x-5}##, then what is ##f^{-1}\circ g^{-1}(3)## ?

    a) -2
    b) -3
    c) -4
    d) -5
    e) -6

    3. The attempt at a solution

    I think the f inverse and g inverse is
    ##f^{-1}(6x+15)= 2x-1##
    ##g^{-1}(\frac{2x-1}{3x-5})=3x+1##

    and,##f^{-1}\circ g^{-1}(3)=f^{-1}(g^{-1}(3))##

    Then,

    I equate ##\frac{2x-1}{3x-5}=3##
    So, I get x = 2

    So, ##g^{-1}(3)=3(2)+1=7##

    Then, I equate ##6x+15=7##
    And, I get x = 8/6 or 4/3

    So, ##f^{-1}(7)=2(\frac{4}{3})-1=\frac{5}{3}## which does not appear in the options..
    Please help me figure out what's wrong
     
  2. jcsd
  3. Nov 10, 2015 #2
    Let's deal with ##g## first. Let the input (##3x+1##) be equal to ##u##. Then ##x=\frac{u-1}{3}##. So you have g(u) = something, and you have to find that something by expressing the output in terms of ##u##. Then try inverting the function.
     
  4. Nov 10, 2015 #3
    I get ##g(u)=\frac{2u-5}{3u-18}##
    Then ##g^{-1}(x)=\frac{18x-5}{3x-2}##
    So, ##g^{-1}(3)=7##

    Then it'll be ##f^{-1}(7)=\frac{5}{3}##
    The answer is -5 according to the book.. But, it doesn't give me the explanation.. :frown:
     
  5. Nov 10, 2015 #4

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    That should be ##x=-4/3##. Still doesn't give the answer from the book though.
     
  6. Nov 10, 2015 #5
    Yup, perhaps the question is wrong
     
  7. Nov 10, 2015 #6

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    Or I'm missing something. I redid your calculation, and also did it like @PWiz suggested (for the two functions), but with both methods I get ##-11/3## as result.
     
  8. Nov 10, 2015 #7
    I just did the calculation myself. I'm getting -11/3 as the answer. I'm guessing something is wrong with the answer given.
    EDIT: I see that @Samy_A has gotten the same result. That pretty much confirms that something is wrong with the question, since we both can't get the same wrong answer.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Inverse and composition of functions
  1. Composite functions (Replies: 3)

  2. Composite functions (Replies: 21)

  3. Composition functions (Replies: 14)

Loading...