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What is (f+g)(x)(f + g)(x)?\newlinef(x)=2x+5f(x) = 2x + 5\newlineg(x)=−x2g(x) = -x^2\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)=2x+5f(x) = 2x + 5\newlineg(x)=−x2g(x) = -x^2\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. Given Functions: We have: \newlinef(x)=2x+5f(x) = 2x + 5 \newlineg(x)=−x2g(x) = -x^2 \newlineNow, we need to add these two functions to find (f+g)(x)(f + g)(x).\newline(f+g)(x)=(2x+5)+(−x2)(f + g)(x) = (2x + 5) + (-x^2)
  3. Simplify Expression: Simplify the expression by combining like terms. Since there are no like terms to combine in this case, we just write the expression in standard polynomial form, which is to have the terms in descending order of their degree. (f+g)(x)=−x2+2x+5(f + g)(x) = -x^2 + 2x + 5

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