IMHO, the answer to (b) is not an infinite number. As for part (a) the anwer is not

, so here the anwer is not as simple as it seems.

My way of thinking is as follows:

We must recall that the assumption from (a) does not work here, and we still do not know function

. We also do not know the dimensionality of the datapoint in the input space

but we know that this input space is fixed (all

for

are already set). In this case we have

of size N generated in a deterministic way, and

(

) is not affected by any noise. So, how many possible

can 'generate'

? The subtle point in this case is the assumption: “For a fixed

of size

”, which means that

is already generated. We can calculate how many possible outputs

for

we can get? Only 1. But there are remaining

datapoints for which we can have

possible values

. So, the anwer is

.

Am I wrong?