Family functions

**dhiab** · July 27th 2009, 07:15 AM

Find the set here this functions is definite :

know :

**red_dog** · July 27th 2009, 07:51 AM

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 $f(\sin x)$ :

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

**dhiab** · July 27th 2009, 11:27 AM

Originally Posted by red_dog

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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