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!

Homework Help: Proving a function is continuous

  1. Oct 21, 2005 #1
    I am working to prove that this function is continuous at [itex] x = 2 [/itex]

    [tex] {f(x) = 9x - 7} [/tex]

    To do this I know that I have to show that [itex] \vert f(x) – f(a) \vert < \epsilon [/itex] and that [itex] \vert x - a < \delta \vert [/itex]

    I tried to come up with a relationship between [itex] \vert x - 2 \vert [/itex] and [itex] \epsilon [/itex] so I could get an appropriate number to choose for [itex] \delta [/itex]

    This is as far as I got

    [tex] \vert {f(x) – f(a)} \vert < \epsilon [/tex]
    [tex] \vert {9x – 7} \vert < \epsilon [/tex]

    I’m stuck. All of the examples the text shows give equations where it is easy to factor out the [itex] \vert {x - a} \vert [/itex] term.

    A push in the right direction would be appreciated.
    Last edited: Oct 21, 2005
  2. jcsd
  3. Oct 21, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Wow. First of all, I suggest you use the more conventionnal sign "-" for minus, instead of 8211; :wink:.

    To show a function is continuous at 'a', you must how that the limit as x approaches a is f(a). Here, a = 2 and f(2) = 9(2)-7 = 11. So given e>0, we must find 'd' such that 0<|x-2|<d ==> |9x-7 - 11|=|9x-18|=9|x-2|<e.

  4. Oct 22, 2005 #3
    Thanks. Latex was being weird yesterday. I'm not sure why it put the 8211; in there in place of some - but not all. Weird.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook