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Math Help - determine f(sqrt(2))?

  1. #1
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    determine f(sqrt(2))?

    Suppose f:R->R is continuous and f(r)= r^2 for each rational number r. Determine f( \sqrt{2}) and justify your conclusions.

    I have no clue
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  2. #2
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    Quote Originally Posted by tn11631 View Post
    Suppose f:R->R is continuous and f(r)= r^2 for each rational number r. Determine f( \sqrt{2}) and justify your conclusions
    If f:\mathbb{R}\to\mathbb{R} is continuous then if (x_n)\to x_0 then it is the case that f\left(x_n\right)\to f\left(x_0\right) .
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    Quote Originally Posted by Plato View Post
    If f:\mathbb{R}\to\mathbb{R} is continuous then if (x_n)\to x_0 then it is the case that f\left(x_n\right)\to f\left(x_0\right) .
    so wait does that just mean it would be 2? And would we have to show it by showing that the limit of lim_r-> \sqrt{2} f(r)=2 which is equal to f( \sqrt{2})..Or can we say that since it is continuous we know that lim as r-> \sqrt{2} of f(r)=f( \sqrt{2})? which is why we know its 2? I hope its not getting confusing.
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