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Question on lim x→2 f(4x^2 − 11) = 8?

  1. Jun 29, 2016 #1
    1. The problem statement, all variables and given/known data

    Determine whether the statement is true or false.
    If f is continuous at 5 and f(5) = 8 and f(4) = 3, then
    lim x→2 f(4x^2 − 11) = 8.

    2. Relevant equations

    lim x->a f(x) = f(a)

    3. The attempt at a solution

    I think the answer to this question is false because limit of f(4x^2 − 11) has to be approaching 8 but I am not sure if this is the right way ti think about this.
     
  2. jcsd
  3. Jun 30, 2016 #2

    andrewkirk

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    Write ##x\mapsto f(4x^2 − 11)## as the composition of two functions ##f## and ##g##, where ##g(x)=4x^2-11##.
    Is ##g## continuous?
    What can we say about the composition of two continuous functions?
     
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