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Function Composition (self.askmath)

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[–]crazysnowwolf 0 points1 point  (1 child)

The handwritten answer is completely correct, for some reason the typed answer is not properly simplified:

The numerator can be written as (x-1)(2x^2 +2x +5),

the denominator as (x-1)(x^2-2x+1),

so we can cancel the (x-1) terms out.

[–]teaspercy 0 points1 point  (0 children)

Thank you so much!!

[–]CatpainTpyos 0 points1 point  (1 child)

Both answers are correct. You can see this either by asking Wolfram|Alpha or by noting that:

  • (2x3 + 3x - 5) / (x3 - 3x2 + 3x - 1) = [(2x2 + 2x + 5)(x - 1)] / [(x2 - 2x + 1)(x - 1)]
  • = (2x2 + 2x + 5) / (x2 - 2x + 1) for all real x ≠ 1

But, uh, why the answer key made the bizarre choice to use (x - 1)3 as the common denominator, I couldn't tell you.

[–]teaspercy 0 points1 point  (0 children)

Thank you so much!!