Suppose we have a simple neural network as follows:

f = NetChain[ { LinearLayer[32], ElementwiseLayer["ReLU"], LinearLayer[16], ElementwiseLayer["ReLU"], LinearLayer[1] }, "Input" -> 3, "Output" -> 1 ] 

How can we represent the function g as neural network that behaves as the function below?

g[v_] := Max@Map[f[Append[v, #]] &, Range[10000]]