Modulus function

Q. If $f\left(x\right)=|x-1|,$ then which of the following are true?

1. $f\left(x^2\right)=\left(f\right(x){)}^2$
2. $f(x+y)=f\left(x\right)+f\left(y\right)$
3. $f\left(|x|\right)=|f\left(x\right)|$
4. None of the above

Q. If x satisfies $\left(x-1\right|+\left(x-2\right|+\left(x-3\right|\ge 6$, then the values of x lie in the range

1. $0\le x\le 4$
2. $x\le -2orx\ge 4$
3. $x\le 0orx\ge 4$
4. $x\le 1orx\ge 4$

Q.

Find the number of integers satisfying the condition |x-3| $>$ 5 and |x + 1 | $\le$ 4

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Q.

How many integers satisfy the relation |x - 1|$\le$ 2

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Q.

Find the number of integers satisfying the condition $|x-3|$$>$ 5 and $|x+1|$ $\le$ 4

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