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What is (f+g)(x)(f + g)(x)?\newlinef(x)=−4xf(x) = -4x\newlineg(x)=2x+5g(x) = 2x + 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)=−4xf(x) = -4x\newlineg(x)=2x+5g(x) = 2x + 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)=−4xf(x) = -4x \newlineg(x)=2x+5g(x) = 2x + 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)=−4x+(2x+5)(f + g)(x) = -4x + (2x + 5)
  3. Simplify Expression: Simplify the expression by combining like terms.\newline(f+g)(x)=−4x+2x+5(f + g)(x) = -4x + 2x + 5\newline(f+g)(x)=(−4x+2x)+5(f + g)(x) = (-4x + 2x) + 5\newline(f+g)(x)=−2x+5(f + g)(x) = -2x + 5

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