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Is the estimate \(\displaystyle \frac{1}{n} \sum_{i}^{n} f(Xi)\) always unbiased for \(\displaystyle \frac{1}{N} \sum_{i}^{N} f(xi)\) no matter what f is?

My thinking: I don't think all f's are unbiased, because not all sample parameters (ex: variance, or s^2) are unbiased for the population parameter (unless they are corrected for finite population sampling). I am confused if I am interpreting the question correctly, i.e f refers to parameters we can kind about the population :(

Thank you for your help in advance!