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Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a continuous function satisfying $\mathrm{f}(\mathrm{x})=\mathrm{x}+\int_{0}^{\mathrm{x}} \mathrm{f}(\mathrm{t}) \mathrm{dt}$, for all $\mathrm{x} \in \mathrm{R}$. Then the number of elements in the set $\mathrm{S}=\{\mathrm{x} \in \mathrm{R} ; \mathrm{f}(\mathrm{x})=0\}$ is-
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$\quad \mathrm{f}^{\prime}(\mathrm{x})=1+\mathrm{f}(\mathrm{x}) \Rightarrow \mathrm{f}(\mathrm{x})=\mathrm{e}^{\mathrm{x}}-1$
$\mathrm{f}(\mathrm{x})=0 \Rightarrow \mathrm{e}^{\mathrm{x}}=1 \quad \mathrm{x}=0 \quad$ One solution
$\mathrm{f}(\mathrm{x})=0 \Rightarrow \mathrm{e}^{\mathrm{x}}=1 \quad \mathrm{x}=0 \quad$ One solution
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