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What is (f+g)(x)(f + g)(x)?\newlinef(x)=3xf(x) = 3x\newlineg(x)=3x2+4xg(x) = 3x^2 + 4x\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)=3xf(x) = 3x\newlineg(x)=3x2+4xg(x) = 3x^2 + 4x\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)=3xf(x) = 3x \newlineg(x)=3x2+4xg(x) = 3x^2 + 4x \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)=3x+(3x2+4x)(f + g)(x) = 3x + (3x^2 + 4x)
  3. Combine Like Terms: Combine like terms to simplify the expression.\newlineSince there are no like terms between 3x3x and 3x23x^2, we just write them next to each other. The like terms 3x3x and 4x4x can be combined.\newline(f+g)(x)=3x2+(3x+4x)(f + g)(x) = 3x^2 + (3x + 4x)\newline(f+g)(x)=3x2+7x(f + g)(x) = 3x^2 + 7x

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