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What is (f+g)(x)(f + g)(x)?\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=−4x+5g(x) = -4x + 5\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Full solution

Q. What is (f+g)(x)(f + g)(x)?\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=−4x+5g(x) = -4x + 5\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Identify Formula: Identify the formula for (f+g)(x)(f + g)(x).(f+g)(x)(f + g)(x) is the sum of f(x)f(x) and g(x)g(x).(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)
  2. Add Functions: We have: \newlinef(x)=−3x2f(x) = -3x^2 \newlineg(x)=−4x+5g(x) = -4x + 5 \newlineNow, we need to add these two functions to find (f+g)(x)(f + g)(x).\newline(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)\newline(f+g)(x)=−3x2+(−4x+5)(f + g)(x) = -3x^2 + (-4x + 5)
  3. Simplify Expression: Simplify the expression by combining like terms. Since there are no like terms to combine in this case, the expression is already in its simplest form. (f+g)(x)=−3x2−4x+5(f + g)(x) = -3x^2 - 4x + 5

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