Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Proving these two functions intersect at 'a'

  1. Sep 25, 2016 #1
    Through experimental observations, I have found that the two functions ##f\left(x\right)=x^{a\left(a-x^3\right)}-a## and ##g\left(x\right)=a^{x\left(x-a^3\right)}-x## will always intersect at ##a## when ##x>0##. Is there a way to mathematically prove this? For instance, simultaneously solving the functions and simplifying the answer down to ##x=a## (Note: the functions sometimes also intersect at other locations besides ##[a, f(a)]##)
     
  2. jcsd
  3. Sep 25, 2016 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You mean prove that ##f(a) = g(a)##?
     
  4. Sep 25, 2016 #3
    Ah yes, expressing it that way does seem a lot clearer.
     
  5. Sep 25, 2016 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Isn't that obvious if you just plug in a for x?
     
  6. Sep 25, 2016 #5
    Right, so it was midnight when I posted this and I wasn't in the most clear mindset. Looking back on this now I can see that by proving ##f(a)=g(a)## you also prove that ##f(x)## intersects ##g(x)## at ##x=a##. Sorry for this entire post.
     
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: Proving these two functions intersect at 'a'
Loading...