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Math Help - Family functions

  1. #1
    Super Member dhiab's Avatar
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    Family functions

    Find the set here this functions is definite :


    know :
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  2. #2
    MHF Contributor red_dog's Avatar
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    For f(x):

    -2x^2-x+1\geq 0\Rightarrow x\in\left[-1,\frac{1}{2}\right]

    For f(\ln x):

    -1\leq\ln x\leq\frac{1}{2}\Rightarrow x\in\left[\frac{1}{e},\sqrt{e}\right]

    For f(\sin x):

    -1\leq\sin x\leq\frac{1}{2}\Rightarrow x\in\left[2k\pi,\frac{\pi}{6}+2k\pi\right]\cup\left[\frac{5\pi}{6}+2k\pi,2(k+1)\pi\right], \ k\in\mathbb{Z}
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  3. #3
    Super Member dhiab's Avatar
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    Quote Originally Posted by red_dog View Post
    For f(x):

    -2x^2-x+1\geq 0\Rightarrow x\in\left[-1,\frac{1}{2}\right]

    For f(\ln x):

    -1\leq\ln x\leq\frac{1}{2}\Rightarrow x\in\left[\frac{1}{e},\sqrt{e}\right]

    For f(\sin x):

    -1\leq\sin x\leq\frac{1}{2}\Rightarrow x\in\left[2k\pi,\frac{\pi}{6}+2k\pi\right]\cup\left[\frac{5\pi}{6}+2k\pi,2(k+1)\pi\right], \ k\in\mathbb{Z}
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