Let a function \( f: R \rightarrow R \) be defined as \[ f(x)=\left\{\begin{array}{ccc} \sin x-e...

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Let a function \( f: R \rightarrow R \) be defined as
\[
f(x)=\left\{\begin{array}{ccc}
\sin x-e^{x} & , \quad \text { if } x \leq 0 \\
a+[-x], & , & \text { if } 0x1 \\
2 x-b & , & \text { if } x \geq 1
\end{array}\right.
\]
where \( [x] \) is the greatest integer less than or equal to \( x \). If \( f \) is continuous on \( R \), then \( (a+b) \) is equal to
(a) 3
(b) 4
(c) 5
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