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Thread: Examples of functions of class C^infinity

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

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