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What is (f+g)(x)(f + g)(x)?\newlinef(x)=x+5f(x) = x + 5\newlineg(x)=x2g(x) = x^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)=x+5f(x) = x + 5\newlineg(x)=x2g(x) = x^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). The correct formula is (f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x).
  2. Substitute Values: We have f(x)=x+5f(x) = x + 5 and g(x)=x2g(x) = x^2. Substitute these values into the formula to get (f+g)(x)=(x+5)+x2(f + g)(x) = (x + 5) + x^2.
  3. Simplify Equation: Simplify the equation (f+g)(x)=(x+5)+x2(f + g)(x) = (x + 5) + x^2 to find (f+g)(x)(f + g)(x).\newlineSince addition is commutative, we can rearrange the terms to write the polynomial in standard form, which typically starts with the highest power of xx.\newline(f+g)(x)=x2+x+5(f + g)(x) = x^2 + x + 5

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