We have that $3 \cdot f(x) + 4 \cdot g(x) = h(x)$ where $f(x),$ $g(x),$ and $h(x)$ are all polynomials in $x.$ If the degree of $f(x)$ is $8

We have that \(3 \cdot f(x) + 4 \cdot g(x) = h(x)\) where \(f(x),\) \(g(x),\) and \(h(x)\) are all polynomials in \(x\) If the degree of \(f(x)\) is \(8\) and the degree of \(h(x)\) is \(9\), then what is the minimum possible degree of \(g(x)\)?