Let a function f:R→R be defined as, fx=sinx−ex if x≤0a+-x if 0<x<12x−b if x≥1 Where x is the greatest integer less than or equal to x. If f is continuous on R, then a+b is equal to:

Question

Let a function $f : R \to R$ be defined as, $f (x) = \{\begin{cases} \sin x - e^{x} & if x \leq 0 \\ a + [- x] & if 0 < x < 1 \\ 2 x - b & if x \geq 1 \end{cases}$

Where $[x]$ is the greatest integer less than or equal to $x .$ If $f$ is continuous on $R$ , then $(a + b)$ is equal to:

4

3

2

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Solution

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