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If f(x)=x^(2)-2 and g(x)=x-3, which of the following is equivalent to f(x)-[g(x)]^(2)? Choose 1 answer: (A) -7 (B) -11 (c) 6x-11 (D) x^(4)-2x^(3)+3x^(2)-2x+1

If f(x)=x2−2 f(x)=x^{2}-2 and g(x)=x−3 g(x)=x-3 , which of the following is equivalent to f(x)−[g(x)]2? f(x)-[g(x)]^{2} ? \newlineChoose 11 answer:\newline(A) −7-7\newline(B) −11-11\newline(C) 6x−11 6 x-11 \newline(D) x4−2x3+3x2−2x+1 x^{4}-2 x^{3}+3 x^{2}-2 x+1

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Full solution

Q. If f(x)=x2−2 f(x)=x^{2}-2 and g(x)=x−3 g(x)=x-3 , which of the following is equivalent to f(x)−[g(x)]2? f(x)-[g(x)]^{2} ? \newlineChoose 11 answer:\newline(A) −7-7\newline(B) −11-11\newline(C) 6x−11 6 x-11 \newline(D) x4−2x3+3x2−2x+1 x^{4}-2 x^{3}+3 x^{2}-2 x+1
  1. Write Given Functions: First, let's write down the given functions and the expression we need to find the equivalent for:\newlinef(x)=x2−2f(x) = x^2 - 2\newlineg(x)=x−3g(x) = x - 3\newlineWe need to find the equivalent of f(x)−[g(x)]2f(x) - [g(x)]^2.
  2. Calculate [g(x)]2[g(x)]^2: Now, let's calculate [g(x)]2[g(x)]^2:
    [g(x)]2=(x−3)2[g(x)]^2 = (x - 3)^2
    [g(x)]2=x2−6x+9[g(x)]^2 = x^2 - 6x + 9
  3. Subtract [g(x)]2[g(x)]^2 from f(x)f(x): Next, we subtract [g(x)]2[g(x)]^2 from f(x)f(x):f(x)−[g(x)]2=(x2−2)−(x2−6x+9)f(x) - [g(x)]^2 = (x^2 - 2) - (x^2 - 6x + 9)
  4. Combine Like Terms: We simplify the expression by combining like terms: f(x)−[g(x)]2=x2−2−x2+6x−9f(x) - [g(x)]^2 = x^2 - 2 - x^2 + 6x - 9
  5. Simplify Expression: After simplifying, we get: f(x)−[g(x)]2=6x−11f(x) - [g(x)]^2 = 6x - 11

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