f(x) Transforms to [f([x])]

Q.

Find the domain and range of $5\sin \left(x-\frac{\mathrm{\pi }}{6}\right)$

Q. The number of solutions for $[\left[x\right]-x]=\sin x$ is (where $[.]$ denotes the greatest integer function) is

1. $5$
2. $7$
3. $0$
4. infinite

Q. $f\left(x\right)=\{\begin{array}{c}0x<1\\ 2x-2x\ge 1\end{array}$, then the number of solution(s) to the equation $f\left(x\right)=x$ is:

1. $2$
2. $1$
3. $4$
4. $0$

Q. The number of solutions for $[\left[x\right]-x]=\sin x$ is (where $[.]$ denotes the greatest integer function) is

1. $7$
2. $5$
3. $0$
4. infinite

Q. The number of solutions for $[\left[x\right]-x]=\sin x$ is (where $[.]$ denotes the greatest integer function) is

1. $5$
2. $7$
3. $0$
4. infinite

Q. The number of solutions for $[\left[x\right]-x]=\sin x$ is (where $[.]$ denotes the greatest integer function) is

1. $5$
2. $7$
3. $0$
4. infinite

Q. The number of solutions for $[\left[x\right]-x]=\sin x$ is (where $[.]$ denotes the greatest integer function) is

1. $5$
2. $7$
3. $0$
4. infinite