= Solution
A function in the stated network class has the form
$$
f(x)=\sum_{j=1}^m\alpha_j\operatorname{sgn}(x^T\beta_j).
$$
Thus this is the class $\mathcal F_2$ from part (d), with the hidden-unit class
$$
\mathcal G=\mathcal H_{\mathcal F_1}.
$$
Parts (c) and (d) give
$$
\begin{aligned}
s(\mathcal H_{\mathcal F_3},n)
&\leq(n+1)^m s(\mathcal G,n)^m\\
&\leq(n+1)^m\bigl((n+1)^p\bigr)^m\\
&=\boxed{(n+1)^{(p+1)m}}.
\end{aligned}
$$
This is the <growth bound for a single-hidden-layer sign network>.
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