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If f(x)=3x^2 - 2x + 6, what is f(x-1).

My answer is continuously f(x-1) = 3x^2 -2x +11, but every site I’ve checked, including the back of the textbook it says the correct answer is 3x^2 -8x + 11. Please help, thank you!

4 Answers

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Textbook's answer is correct. I have a feeling that you are not expanding (x - 1)^(2) correctly.

Note that:

f(x - 1)

= 3 (x - 1)^(2) \- 2(x - 1) + 6

= 3 (x^(2) \- 2x + 1) - 2x + 2 + 6

= 3x^(2) \- 6x + 3 - 2x + 2 + 6

= 3x^(2) \- 8x + 11
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You can do simple checks to see if you have the right answer.

Let's say x = 1, then x-1 = 0, f(x-1) = f(0) =6

Now, substitute x = 1 in your formula and see if it matches with 6. Does the textbook answer match?
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Remember that

3(x-1)^2 = 3x^2 -6x +3
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Let me see...

3(x-1)(x-1) - 2(x-1) + 6

(3x -3)(x-1) -2x +2 +6

3×^2 - 3x -3x +3 - 2x +8

3×^2 -8× + 11

Does that look right?
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