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.

Let $$f(x) = \left\{ {\matrix{ {{{{e^x} - 1} \over x},} & {x > 0} \cr {0,} & {x = 0} \cr } } \right.$$, be a real valued function, then which of the following statements is/are correct?

I. f(x) is right continuous at x = 0

II. f(x) is discontinuous at x = 1

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Consider the equation x + | y | = 2y.

Which of the following statements are not correct?

1. y as a function of x is not defined for all real x.

2. y as a function of x is not continuous at x = 0.

3. y as a function of x is differentiable for all x.

Select the correct answer using the codes given below.

Consider the equation x + | y | = 2y.

What is the derivative of y as a function of x with respect to x for x < 0 ?