Confusion with Notation in the Book on Deep Learning by Ian Goodfellow et al
Let $\mathbf{y}  = \mathbf{W}^T \mathbf{x}$
Then, $\mathbf{y}^T =(\mathbf{W}^T \mathbf{x})^T =\mathbf{x}^{T}(W^T)^T = \mathbf{x}^{T}W $. Note that $\mathbf{W}$ does not have to be a square matrix.
Let $e^{(i)}_{j} = \delta_{i,j} $.
Then,  $y_{i} = \mathbf{y}^{T}e^{(i)} = (\mathbf{x}^T W) e^{(i)} = \mathbf{x}^{T}(We^{(i)}) = \mathbf{x}^{T}W_{:,i}$
and thus
$h_{i} = g(\mathbf{x}^T W_{:,i}+c_{i}) = g(y_{i}+c_{i})$
On the other hand,
$f(..)  = w^{T} \max\{\mathbf{0},W^{T}\mathbf{x}+\mathbf{c}\}+b = w^{T} \max\{\mathbf{0},\mathbf{y}+\mathbf{c}\}+\mathbf{b}$.
Does that answer your question ?