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What is (f+g)(x)(f + g)(x)?\newlinef(x)=x+2f(x) = x + 2\newlineg(x)=−xg(x) = -x\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)=x+2f(x) = x + 2\newlineg(x)=−xg(x) = -x\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. Calculate sum: We have: \newlinef(x)=x+2f(x) = x + 2 \newlineg(x)=−xg(x) = -x\newlineNow, we need to 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)=(x+2)+(−x)(f + g)(x) = (x + 2) + (-x)
  3. Simplify expression: Simplify the expression by combining like terms.\newline(f+g)(x)=x+2−x(f + g)(x) = x + 2 - x\newlineThe xx and −x-x cancel each other out, so we are left with:\newline(f+g)(x)=2(f + g)(x) = 2

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