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What is (f+g)(x)(f + g)(x)?\newlinef(x)=3x2f(x) = 3x^2\newlineg(x)=−3x2+6xg(x) = -3x^2 + 6x\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)=−3x2+6xg(x) = -3x^2 + 6x\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 ff and gg: We have:\newlinef(x)=3x2f(x) = 3x^2\newlineg(x)=−3x2+6xg(x) = -3x^2 + 6x\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)=3x2+(−3x2+6x)(f + g)(x) = 3x^2 + (-3x^2 + 6x)
  3. Simplify expression: Simplify the expression by combining like terms.\newline(f+g)(x)=3x2−3x2+6x(f + g)(x) = 3x^2 - 3x^2 + 6x\newline(f+g)(x)=0x2+6x(f + g)(x) = 0x^2 + 6x\newline(f+g)(x)=6x(f + g)(x) = 6x

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