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What is (f+g)(x)(f + g)(x)?\newlinef(x)=xf(x) = x\newlineg(x)=−2x+2g(x) = -2x + 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)=xf(x) = x\newlineg(x)=−2x+2g(x) = -2x + 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)=xf(x) = x \newlineg(x)=−2x+2g(x) = -2x + 2 \newlineNow, we need to find the sum of these two functions.\newline(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)\newline(f+g)(x)=x+(−2x+2)(f + g)(x) = x + (-2x + 2)
  3. Simplify Expression: Simplify the expression by combining like terms.\newline(f+g)(x)=x−2x+2(f + g)(x) = x - 2x + 2\newline(f+g)(x)=−x+2(f + g)(x) = -x + 2\newlineThis is the simplified form of the function (f+g)(x)(f + g)(x).

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