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Math Help - Examples of functions of class C^infinity

  1. #1
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    Examples of functions of class C^infinity

    Examples of functions f,g:\mathbb{R}\to\mathbb{R} of class C^\infty that satisfy:
    (1) f(x)=0\Leftrightarrow 0\leq x\leq 1;
    (2) g(x)=x if |x| \leq 1, and |g(x)|<|x| if |x|>1
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  2. #2
    Senior Member Tinyboss's Avatar
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    Look into "bump functions".
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