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What is (f+g)(x)(f + g)(x)?\newlinef(x)=3xf(x) = 3x\newlineg(x)=5x+2g(x) = 5x + 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)=3xf(x) = 3x\newlineg(x)=5x+2g(x) = 5x + 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. Add Functions: We have: \newlinef(x)=3xf(x) = 3x \newlineg(x)=5x+2g(x) = 5x + 2 \newlineNow, we need to add these two functions to find (f+g)(x)(f + g)(x).\newline(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)\newline(f+g)(x)=3x+(5x+2)(f + g)(x) = 3x + (5x + 2)
  3. Combine Like Terms: Combine the like terms to simplify the expression.\newline(f+g)(x)=3x+5x+2(f + g)(x) = 3x + 5x + 2\newline(f+g)(x)=(3x+5x)+2(f + g)(x) = (3x + 5x) + 2\newline(f+g)(x)=8x+2(f + g)(x) = 8x + 2

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