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Math Help - Points of continuity

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    Points of continuity

    How would you find the points of continuity of this function
    f(x) := \frac{x^2 + 2x + 1}{x^2+1}
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by CrazyCat87 View Post
    How would you find the points of continuity of this function
    f(x) := \frac{x^2 + 2x + 1}{x^2+1}
    If f is continuous and g is continuous then f+g is continuous. Similarly, if \frac{f}{g} is continuous if g(x)\ne 0,\text{ }\forall x\in\mathbb{R}
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    Not really sure what you meant to say here, but since both the numerator and denominator are polynomials and all polynomials are continuous, then would
    f(x) := \frac{x^2 + 2x + 1}{x^2+1} be continuous everywhere?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by CrazyCat87 View Post
    Not really sure what you meant to say here, but since both the numerator and denominator are polynomials and all polynomials are continuous, then would
    f(x) := \frac{x^2 + 2x + 1}{x^2+1} be continuous everywhere?
    After noting that x^2+1\ne0 then
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  5. #5
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    haha of course!! thanks
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