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Let a function f : R $$\to$$ R be defined as $$f(x) = \left\{ {\begin{matrix} {\sin x - {e^x}} & {if} & {x \le 0} \\ {a + [ - x]} & {if} & {0 < x < 1} \\ {2x - b} & {if} & {x \ge 1} \\ \end{matrix} } \right.$$ where [ x ] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to:

JEE · Math · previous-year question

  1. A.4
  2. B.3correct
  3. C.2
  4. D.5

Answer

B. 3

Explanation

Continuous x = 0 f(0+) = f(0$$-$$) $$\Rightarrow$$ a $$-$$ 1 = 0 $$-$$ e0 $$\Rightarrow$$ a = 0 Continuous at x = 1 f(1+) = f(1$$-$$) $$\Rightarrow$$ 2(1) $$-$$ b = a + ($$-$$1) $$\Rightarrow$$ b = 2 $$-$$ a + 1 $$\Rightarrow$$ b = 3 $$\therefore$$ a + b = 3

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