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Statement-1: $f (x) = {\sin x} - {\cos x}$ is discontinuous at $x = π / 2,$ ${x}$ is the fractional part of x.
Statement-2: Sum of two discontinuous function is a discontinuous function

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(b) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for

STATEMENT-1 is False, STATEMENT-2 is True

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

answer is C.

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Detailed Solution

$\begin{aligned} lim_{x \to π / 2 +} f (x) = 0 - 0 = 0 \\ lim_{x \to π / 2 -} f (x) = 1 - 0 = 1 \end{aligned}$

$f$ is discontinuous at $x = π / 2 .$ But sum of two discontinuous need not be discontinuous e .g.

$\begin{array}{l} f (x) = \{\begin{array}{cc} 1 & , x \geq 0 \\ - 1 & , x < 0 \end{array} g (x) = \{\begin{array}{cc} - 1 & , x \geq 0 \\ 1 & , x < 0 \end{array} \\ f (x) + g (x) = 0 for all x . \end{array}$

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