represent some set to a functional form show example

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Let say we have a set k $\subset R$

K = [a,b) for convenient k = $[0,\infty)$,

How do we represent some function such as $f:K \to R$

can we represent f:k like y= ..... ??

or we can only represent the some function f:k to a subset.

sorry for little confuse of the question. but i'm also confuse that my question is valid or not