​$$\text{Let } (X, d) \text{ be a metric space and let } f: X \to X \text{ be a function such that:}\\d(f(x), f(y)) \leq d(x, y), \quad \text{for every } x, y \in X.\\\text{Which of the following statements is necessarily true?}$$​​

Correct option is A

​$$d(f(x), f(y)) \leq d(x, y), \; \forall \, x, y \in X.\ \text{is given}\\\implies \forall \, \epsilon > 0, \, \exists \, \delta >0 \text{ for any } c \in X \text{ such that }\\d(f(x), f(c)) < \epsilon \; \text{whenever} \; d(x, c) < \delta.\\\text{Thus, } f(x) \text{ is a continuous function.}$$​​