Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$(g-f)(x)=x^2-8x+12$
We know that $(g-f)(x)=g(x)-f(x)$. Substituting the values, we get \begin{align} (g-f)(x)&=(x^2-3x+4)-(5x-8) \\ &= x^2-3x+4-5x+8 \\ &= x^2-8x+12\end{align}