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What is (f−g)(x)(f - g)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=−x2+4g(x) = -x^2 + 4\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f−g)(x)(f - g)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=−x2+4g(x) = -x^2 + 4\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Substitute functions into expression: We have f(x)=2xf(x) = 2x and g(x)=−x2+4g(x) = -x^2 + 4. Let's write down the expression for (f−g)(x)(f - g)(x) by substituting the given functions:\newline(f−g)(x)=f(x)−g(x)=(2x)−(−x2+4)(f - g)(x) = f(x) - g(x) = (2x) - (-x^2 + 4).
  2. Simplify by distributing: Now, we simplify the expression by distributing the negative sign across the terms in g(x)g(x):(f−g)(x)=2x−(−x2)−4=2x+x2−4.(f - g)(x) = 2x - (-x^2) - 4 = 2x + x^2 - 4.
  3. Arrange terms in standard form: We should arrange the terms in descending order of the powers of xx to write the polynomial in standard form: (f−g)(x)=x2+2x−4(f - g)(x) = x^2 + 2x - 4.

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