1. ## Family functions

Find the set here this functions is definite :

know :

2. For $\displaystyle f(x)$:

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

For $\displaystyle f(\ln x)$:

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

For $\displaystyle f(\sin x)$:

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

3. Originally Posted by red_dog
For $\displaystyle f(x)$:

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

For $\displaystyle f(\ln x)$:

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

For $\displaystyle f(\sin x)$:

$\displaystyle -1\leq\sin x\leq\frac{1}{2}\Rightarrow x\in\left[2k\pi,\frac{\pi}{6}+2k\pi\right]\cup\left[\frac{5\pi}{6}+2k\pi,2(k+1)\pi\right], \ k\in\mathbb{Z}$
Hello and Thank you
Have you the detail For .