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What is (f−g)(x)(f - g)(x)?\newlinef(x)=4x+5f(x) = 4x + 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)=4x+5f(x) = 4x + 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)=4x+5f(x) = 4x + 5 and g(x)=x2g(x) = x^2. Substitute these values into the formula to get (f−g)(x)=(4x+5)−(x2)(f - g)(x) = (4x + 5) - (x^2).
  3. Simplify Equation: Simplify the equation (f−g)(x)=(4x+5)−(x2)(f - g)(x) = (4x + 5) - (x^2) to find (f−g)(x)(f - g)(x).\newline(f−g)(x)=4x+5−x2(f - g)(x) = 4x + 5 - x^2\newlineSince subtraction is distributive over addition, we can rewrite this as:\newline(f−g)(x)=−x2+4x+5(f - g)(x) = -x^2 + 4x + 5

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