Answer:To find \((f+h)(x)\), you need to add the functions \(f(x)\) and \(h(x)\). Let's work with the given functions:1. \( f(x) = 2x^2 - 4x + 3 \)2. \( h(x) = 3x^2 + 6x - 9 \)To find \((f+h)(x)\), you add the two functions together:\[(f+h)(x) = f(x) + h(x)\]Substitute the given functions:\[(f+h)(x) = (2x^2 - 4x + 3) + (3x^2 + 6x - 9)\]Combine like terms:\[(f+h)(x) = (2x^2 + 3x^2) + (-4x + 6x) + (3 - 9)\]\[(f+h)(x) = 5x^2 + 2x - 6\]So, the function \((f+h)(x)\) is:\[(f+h)(x) = 5x^2 + 2x - 6\]Step-by-step explanation: