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Math Help - Question about a function

  1. #1
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    Question about a function

    Here's the question:
    Let R be the set of real numbers and let f be the function from R to R defined by
    f(x) = 1/[(x^2)+1] for all x in R
    Let C= {r in R|r<(1/5)}.
    Find the set f^-1 (C)

    From what I understand, I get:
    f^-1(C)={x in R|[1/[(x^2)+1]] < (1/5)
    I'm not sure if that is even close to being correct, but after I get to this point, I have no clue where to go with it.
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  2. #2
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    Quote Originally Posted by lisaak View Post
    Here's the question:
    Let R be the set of real numbers and let f be the function from R to R defined by
    f(x) = 1/[(x^2)+1] for all x in R
    Let C= {r in R|r<(1/5)}.
    Find the set f^-1 (C)
    Watch frum die meister.

    f:\mathbb{R}\to \mathbb{R}
    Und,
    f(x)=\frac{1}{1+x^2}.
    We have,
    C=(-\infty,1/5)
    Thus,
    f^{-1}[C]=\{x\in \mathbb{R}|f(x)\in (-\infty,1/5)\}
    That means, find all x\in \mathbb{R}
    Such as,
    \frac{1}{1+x^2}<1/5
    Since both sides are positive you can take reciprocals and flip the signs (a trick not taught in schools)
    1+x^2>5
    Equivalently,
    x^2>4
    Equivalently,
    |x|<2
    Thus,
    f^{-1}[C]=(-2,2)
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