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What is (f+g)(x)(f + g)(x)?\newlinef(x)=x2f(x) = x^2\newlineg(x)=x+4g(x) = x + 4\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)=x2f(x) = x^2\newlineg(x)=x+4g(x) = x + 4\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 Functions: We have: \newlinef(x)=x2f(x) = x^2 \newlineg(x)=x+4g(x) = x + 4 \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)=x2+(x+4)(f + g)(x) = x^2 + (x + 4)
  3. Combine Like Terms: Combine the like terms to simplify the expression.\newlineSince there are no like terms to combine with x2x^2, the expression is already in its simplest form.\newline(f+g)(x)=x2+x+4(f + g)(x) = x^2 + x + 4

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