Let f(x) = [x], where [ . ] is the greatest integer function and g(x) = sin x be two real valued functions over R.

Which of the following statements are correct?

I. (fof) (x) = f(x).

II. (gog) (x) = g(x) only when x = 0.

III. (go(fog)) (x) can taken only three values.

Select the correct answer using the code given below.

Let $$f(x) = \left\{ {\matrix{ { - 2,} & { - 3 \le x \le 0} \cr {x - 2,} & {0 < x \le 3} \cr } } \right.$$ and $$g(x) = f(|x|) + |f(x)|$$.

Which of the following statements is/are correct?

I. g(x) is differentiable at x = 0

II. g(x) is differentiable at x = 2.

Select the correct answer using the code given below.

Let $$f(x) = \left\{ {\matrix{ { - 2,} & { - 3 \le x \le 0} \cr {x - 2,} & {0 < x \le 3} \cr } } \right.$$ and $$g(x) = f(|x|) + |f(x)|$$.

What is the value of the differential coefficient of g(x) at x = $$-$$2 ?

Let $$f(x) = \left\{ {\matrix{ { - 2,} & { - 3 \le x \le 0} \cr {x - 2,} & {0 < x \le 3} \cr } } \right.$$ and $$g(x) = f(|x|) + |f(x)|$$.

Which of the following statements are correct?

I. g(x) is continuous at x = 0.

II. g(x) is continuous at x = 2.

III. g(x) is continuous at x = $$-$$1.

Select the correct answer using the code given below.