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 functions

  1. Aug 17, 2015 #1
    Is there a way to formally prove that if ##f## and ##g## are multiplicative inverses of each other, then ##f^{-1} (x) = g^{-1} (\frac{1}{x})##?
     
  2. jcsd
  3. Aug 17, 2015 #2
    I'd start by testing a number of special cases and see what approach the trickier special cases suggest.

    Simple special cases almost never suggest approaches to proof, but the tricky special cases often do.
     
  4. Aug 17, 2015 #3

    pasmith

    User Avatar
    Homework Helper

    Let [itex]h[/itex] be the function which takes [itex]x[/itex] to [itex]1/x[/itex]. Now if [itex]f(x)g(x) = 1[/itex] for all [itex]x[/itex] then [itex]f = h \circ g[/itex]. Then [itex]f^{-1} = g^{-1} \circ h^{-1}[/itex]. But [itex]h = h^{-1}[/itex] so [itex]f^{-1} = g^{-1} \circ h[/itex] as required.
     
  5. Aug 17, 2015 #4
    Perfect. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Inverse functions
  1. Inverse functions (Replies: 3)

  2. Inverse function (Replies: 12)

  3. Inverse of a function (Replies: 6)

  4. Inverse function (Replies: 5)

Loading...