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What is (f+g)(x)(f + g)(x)?\newlinef(x)=−x2f(x) = -x^2\newlineg(x)=x2+5xg(x) = x^2 + 5x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f+g)(x)(f + g)(x)?\newlinef(x)=−x2f(x) = -x^2\newlineg(x)=x2+5xg(x) = x^2 + 5x\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). \newline(f+g)(x)(f + g)(x) is the sum of f(x)f(x) and g(x)g(x). \newline(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)
  2. Calculate Sum: We have: \newlinef(x)=−x2f(x) = -x^2 \newlineg(x)=x2+5xg(x) = x^2 + 5x \newlineNow, let's find (f+g)(x)(f + g)(x) by adding f(x)f(x) and g(x)g(x) together.\newline(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x) \newline(f+g)(x)=(−x2)+(x2+5x)(f + g)(x) = (-x^2) + (x^2 + 5x)
  3. Simplify Expression: Simplify the expression by combining like terms.\newline(f+g)(x)=−x2+x2+5x(f + g)(x) = -x^2 + x^2 + 5x \newline(f+g)(x)=5x(f + g)(x) = 5x

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