Domain

Q. If $h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$, where $f\left(x\right)=x^2-2x$ and $g\left(x\right)=x^3-3x^2+2x,$ then the number of integers which are not present in the domain of ${\left(h\right(x\left)\right)}^{1/1001}$ is

Q.

The domain of the function $f\left(x\right)=\frac{1}{{\log }_{10}(1-x)}+\sqrt{x+2}$ is

1. None of these

2. $]-3,-2.5[\cup ]-2.5,-2[$

3. $]0,1[$

4. $[-2,0[\cup ]0,1[$

Q.

If $x$ satisfies $|x-1|+|x-2|+|x-3|\ge 6$, then

1. $0\le x\le 4$
   

2. $x\le -2$ or $x\ge 4$
   

3. $x\le 0$ or $x\ge 4$
   

4. none of these

Q.

If, $f\left(x\right)=cos\left[{\pi }^2\right]x+cos[-{\pi }^2]x,$ where [x] stands for greatest integer function, then

1. $f(-\pi )=0$

2. $f\left(\frac{\pi }{4}\right)=2$

3. $f\left(\frac{\pi }{2}\right)=1$

4. $f\left(\pi \right)=1$

Q. The domain of the function f(x) given by $f\left(x\right)=\frac{1}{\sqrt{x-\left(x\right]}}$
where [.] is greatest integer function, is

1. Z
2. R
3. $R-Z^{+}$
4. $R-Z$

Q. The domain of the function f(x) defined by
$f\left(x\right)=\frac{1}{{\log }_{10}\left(2-x\right)}+\sqrt{x+2}$is

1. $(-2,1)\cup \left(1,2\right)$
2. $[-2,2]$
3. $[-2,1)\cup (1,2]$
4. $[-2,1)\cup \left(1,2\right)$

Q. The domain of $f\left(x\right)=\sqrt{a^2-x^2}$ (a > 0) is

1. (-a, a)
2. [-a, a]
3. [0, a]
4. (-a, 0]

Q. $\mathrm{The}\mathrm{domain}\mathrm{of}f\left(x\right)={\sin }^{-1}\left(2x^2-3\right],\mathrm{where}[.]\mathrm{denotes}\mathrm{the}\mathrm{greatest}\mathrm{integer}\mathrm{function},\mathrm{is}$

1. $\left(-\sqrt{\frac{3}{2}},\sqrt{\frac{3}{2}}\right)$
2. $(-\sqrt{\frac{3}{2}},-1]\cup \left(-\sqrt{\frac{5}{2}},\sqrt{\frac{5}{2}}\right)$
3. $\left(-\sqrt{\frac{5}{2}},\sqrt{\frac{5}{2}}\right)$
4. $(-\sqrt{\frac{5}{2}},-1]\cup [1,\sqrt{\frac{5}{2}})$

Q. The domain of the function f(x) given by $f\left(x\right)=\frac{1}{\sqrt{x+\left|x\right|}}$ is

1. R
2. $R^{+}$
3. $R^{-}$
4. $R-\{-1\}$

Q. Consider a function $f:(-\infty ,\frac{-A}{8})\cup (\frac{-A}{8},\frac{-B}{8})\to R$ such that $f\left(x\right)=lo{g}_{|x-1|-|x+1|-\frac{1}{2}}(x^2-x-\frac{1}{2}{)}^{x^2-3x+2}$, then the value of $A+B$ is