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Which one of the following statements is TRUE regarding the function $f(x)= frac{1}{x}$

$f$ is continuous on $(0,1)$ but not uniformly continuous on $(0,1)$.

$f$ is uniformly continuous on $(0,1)$ but not continuous on $(0,1)$.

$f$ is both uniformly continuous and continuous on $(0,1)$.

$f$ is not uniformly continuous or continuous on $(0,1)$.