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What is (f−g)(x)(f - g)(x)?\newlinef(x)=−2x2+2f(x) = -2x^2 + 2\newlineg(x)=−2x2g(x) = -2x^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)=−2x2+2f(x) = -2x^2 + 2\newlineg(x)=−2x2g(x) = -2x^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 difference 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. Given Functions: We have:\newlinef(x)=−2x2+2f(x) = -2x^2 + 2\newlineg(x)=−2x2g(x) = -2x^2\newlineNow, let's find (f−g)(x)(f - g)(x) by subtracting g(x)g(x) from f(x)f(x).\newline(f−g)(x)=(−2x2+2)−(−2x2)(f - g)(x) = (-2x^2 + 2) - (-2x^2)
  3. Subtract Functions: Simplify the expression by distributing the negative sign and combining like terms. \newline(f−g)(x)=−2x2+2+2x2(f - g)(x) = -2x^2 + 2 + 2x^2
  4. Simplify Expression: The terms −2x2-2x^2 and +2x2+2x^2 cancel each other out, so we are left with: (f−g)(x)=2(f - g)(x) = 2

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