To find \(g(x)\) in terms of \(f(x)\), we need to apply the given transformations to \(f(x)\).

1. The first transformation is a stretch in the \(x\)-direction by a factor of 0.5. This means we replace \(x\) with \(2x\) in the function \(f(x)\). So, the function becomes \(f(2x)\).

2. The second transformation is a translation by \(\begin{pmatrix} 0 \\ 1 \end{pmatrix}\), which means we add 1 to the entire function. Thus, the function becomes \(f(2x) + 1\).

Therefore, the expression for \(g(x)\) in terms of \(f(x)\) is \(g(x) = f(2x) + 1\).