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assuming certain properties about variables

let's say I have defined the following function:
f[x_?Positive] = x
Now I want to evaluate f with a variable t:
As mathematica knows nothing about t, the output is f[t] instead of t.

How can I tell mathematica, that t should be a positive number so that 
Positive[t] evaluates true and then f[t] evaluates to t?
Of course this is just an example, which should present what I would 
like to know.

Thanks in advance.

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