# Interpretation of feature selection task

So I am given the following question

Data set sample5.txt has a 20-dimensional input $x$ in $\mathbb{R}^{20}$ but we suspect that many of these are actually irrelevant. Could you model the function $y = f(x)$ while - at the same time - figuring which dimensions contribute to the output?

So it is a feature selection task - I understand that. But I'm sort of confused by the

at the same time

part. I know many feature selection algorithms but they do not actually produce models for the data, they just produce decisions regarding which features are important and which are not. Conversely, a model (alone) doesn't really give much information regarding which features are important and which are not.

Perhaps you could do simple linear regression and then select features based on the weights (but I have never heard of anyone doing this). Or do you think that I am over-analyzing the question and what I should do is simply do feature selection first, then create the model?