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What is (f+g)(x)(f + g)(x)?\newlinef(x)=−5xf(x) = -5x\newlineg(x)=4x+5g(x) = 4x + 5\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)=−5xf(x) = -5x\newlineg(x)=4x+5g(x) = 4x + 5\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. Find sum: We have: \newlinef(x)=−5xf(x) = -5x \newlineg(x)=4x+5g(x) = 4x + 5 \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)=−5x+(4x+5)(f + g)(x) = -5x + (4x + 5)
  3. Simplify expression: Simplify the expression by combining like terms.\newline(f+g)(x)=−5x+4x+5(f + g)(x) = -5x + 4x + 5\newline(f+g)(x)=(−5x+4x)+5(f + g)(x) = (-5x + 4x) + 5\newline(f+g)(x)=−x+5(f + g)(x) = -x + 5

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