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Given the function f(x)=-4x^(2)-3, then what is f(x-1) as a simplified polynomial? Answer:

Given the function f(x)=−4x2−3 f(x)=-4 x^{2}-3 , then what is f(x−1) f(x-1) as a simplified polynomial?\newlineAnswer:

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Q. Given the function f(x)=−4x2−3 f(x)=-4 x^{2}-3 , then what is f(x−1) f(x-1) as a simplified polynomial?\newlineAnswer:
  1. Substitute x−1x-1: Substitute (x−1)(x-1) for xx in the function f(x)=−4x2−3f(x)=-4x^2-3.\newlinef(x−1)=−4(x−1)2−3f(x-1) = -4(x-1)^2 - 3
  2. Expand square: Expand the square (x−1)2(x-1)^2.(x−1)2=x2−2x+1(x-1)^2 = x^2 - 2x + 1
  3. Substitute expanded square: Substitute the expanded square into the function.\newlinef(x−1)=−4(x2−2x+1)−3f(x-1) = -4(x^2 - 2x + 1) - 3
  4. Distribute −4-4: Distribute the −4-4 across the terms in the parentheses.\newlinef(x−1)=−4x2+8x−4−3f(x-1) = -4x^2 + 8x - 4 - 3
  5. Combine constant terms: Combine the constant terms −4-4 and −3-3.f(x−1)=−4x2+8x−7f(x-1) = -4x^2 + 8x - 7

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