Consider the following statements in respect of f(x) = |x| - 1

1. f(x) is continuous at x = 1.

2. f(x) is differentiable at x = 0.

Which of the above statements is/are correct?

If $f(x) = \frac{[x]}{|x|}$, x ≠ 0, where [⋅] denotes the greatest integer function, then what is the right-hand limit of f(x) at x = 1?

Consider the following statements in respect of the function $\rm f(x) = sin \left(\frac{1}{x^2}\right)$, x ≠ 0:

1. It is continuous at x = 0, if f(0) = 0.

2. It is continuous at $x = \frac{2}{\sqrt{\pi}}$.

Which of the above statements is/are correct?

What is the range of the function f(x) = 1 - sinx defined on entire real line?