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If 
f(x)=(x-2)^(2)-x^(3), what is 
f(-3)-f(3)?

If f(x)=(x2)2x3 f(x)=(x-2)^{2}-x^{3} , what is f(3)f(3)? f(-3)-f(3) ?

Full solution

Q. If f(x)=(x2)2x3 f(x)=(x-2)^{2}-x^{3} , what is f(3)f(3)? f(-3)-f(3) ?
  1. Calculate f(3)f(-3): First, we need to calculate f(3)f(-3). The function f(x)f(x) is given by f(x)=(x2)2x3f(x) = (x - 2)^2 - x^3. Let's substitute xx with 3-3.\newlinef(3)=((3)2)2(3)3f(-3) = ((-3) - 2)^2 - (-3)^3\newlinef(3)=(5)2(27)f(-3) = (-5)^2 - (-27)\newlinef(3)=25+27f(-3) = 25 + 27\newlinef(3)=52f(-3) = 52
  2. Calculate f(3)f(3): Next, we need to calculate f(3)f(3). Again, we use the function f(x)=(x2)2x3f(x) = (x - 2)^2 - x^3 and substitute xx with 33.\newlinef(3)=(32)233f(3) = (3 - 2)^2 - 3^3\newlinef(3)=(1)227f(3) = (1)^2 - 27\newlinef(3)=127f(3) = 1 - 27\newlinef(3)=26f(3) = -26
  3. Find the difference: Now, we have the values for f(3)f(-3) and f(3)f(3). We need to find the difference f(3)f(3)f(-3) - f(3).\newlinef(3)f(3)=52(26)f(-3) - f(3) = 52 - (-26)\newlinef(3)f(3)=52+26f(-3) - f(3) = 52 + 26\newlinef(3)f(3)=78f(-3) - f(3) = 78

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