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What is (f+g)(x)(f + g)(x)?\newlinef(x)=3x+1f(x) = 3x + 1\newlineg(x)=−x2g(x) = -x^2\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)=3x+1f(x) = 3x + 1\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). The correct formula is (f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x).
  2. Substitute Values: We have f(x)=3x+1f(x) = 3x + 1 and g(x)=−x2g(x) = -x^2. Substitute these values into the formula to get (f+g)(x)=(3x+1)+(−x2)(f + g)(x) = (3x + 1) + (-x^2).
  3. Simplify Equation: Simplify the equation (f+g)(x)=(3x+1)+(−x2)(f + g)(x) = (3x + 1) + (-x^2) to find (f+g)(x)(f + g)(x).\newline(f+g)(x)=−x2+3x+1(f + g)(x) = -x^2 + 3x + 1

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