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Math Help - Find domain of function?

  1. #1
    Super Member fardeen_gen's Avatar
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    Find domain of function?

    Find domain of the function:
    f(x) = \sqrt{\cos \left(\frac{\pi}{x^2}\right)}
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  2. #2
    Senior Member
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    Not so bad...

    \cos(\frac{\pi}{x^2})\geq 0

    \frac{\pi}{x^2}\in[-\frac\pi2+2\pi n,\frac\pi2+2\pi n]

    \frac1{x^2}\in[-\frac12+2n,\frac12+2n]

    x^2\in[\frac1{\frac12+2n},\frac1{-\frac12+2n}]

    x\in\pm [\frac1{\sqrt{\frac12+2n}},\frac1{\sqrt{-\frac12+2n}}]

    So domain D=\cup_{n=1}^\infty [-\frac1{\sqrt{-\frac12+2n}},-\frac1{\sqrt{\frac12+2n}}]\cup[\frac1{\sqrt{\frac12+2n}},\frac1{\sqrt{-\frac12+2n}}]
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