# True / false question about a Cauchy sequence in Real Analysis [duplicate]

I am solving assignments in Real analysis but I am unable to think about how I can solve this question.

Let $$f: ( 0, \infty ) \to \mathbb{R}$$ be a continuous function. Does $$f$$ maps any Cauchy sequence to a Cauchy sequence.

I tried by taking $${x_n}$$ and using |$$x_n$$ - $$x_m$$| <$$\epsilon$$ for all $$n, m > N$$ ( $$N$$ is a natural number) . But how can I formulate the Cauchy sequence property of $$x_n$$ into $$f(x_n$$) ? I am unable to think about it.

take the map $$x \mapsto \frac{1}{x}$$ and the Cauchy sequence $$\{\frac{1}{n}\}_{n \ge 1}$$