... to be the model of a an arbitrary data set defined by vector f (function values) and vector x (data points) for

And we're asked to find the best fit in the least squares sense for this model -- Find the normal equation?

(corrected) where

is the 14th degree Chebyshev polynomial (of the first kind).

You certainly can show HOW to get the normal matrix, and normal equation for this, but you have no specific values for the and no observed dependent values so you certainly can't give a numerical answer.