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# If f(x)=√(x^2−2x+1), what is f(9)?

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Math Expert
Joined: 02 Sep 2009
Posts: 47946
If f(x)=√(x^2−2x+1), what is f(9)?  [#permalink]

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15 Apr 2018, 10:00
00:00

Difficulty:

5% (low)

Question Stats:

96% (00:31) correct 4% (00:20) wrong based on 94 sessions

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If $$f(x)=\sqrt{x^2−2x+1}$$, what is f(9)?

A. -8
B. 5
C. 8
D. 9
E. 82

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If f(x)=√(x^2−2x+1), what is f(9)?  [#permalink]

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15 Apr 2018, 10:30
Bunuel wrote:
If $$f(x)=\sqrt{x^2−2x+1}$$, what is f(9)?

A. -8
B. 5
C. 8
D. 9
E. 82

We'll show two approaches.

The Precise approach involves straight up calculation:
9^2 - 2*9 + 1 = 81 - 18 + 1 = 64, the square root of which is 8.
Note that the 'square root function' always returns a positive number which is why (A) is incorrect.

We could also have estimated the answer, an Alternative approach.
We know that the square root of x^2 is x. Since we're asked for the square root of something smaller than x^2 (e.g. x^2 - 2*x+1) we know the answer must be smaller than x.
Only C and B make sense but we can estimate (without calculating) that (B) is too far: 5^2 = 25 and 81 - 18 + 1 is about 60, much larger than that.
Note that in this case estimation is not necessary as the equation is simple, however it can be very useful for difficult calculations.
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Joined: 15 Apr 2018
Posts: 2
Re: If f(x)=√(x^2−2x+1), what is f(9)?  [#permalink]

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15 Apr 2018, 21:51
1
f(x) = sqrt{(x-1)^2} = x - 1
f(9) = 9 - 1 = 8

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Joined: 04 Apr 2018
Posts: 5
Re: If f(x)=√(x^2−2x+1), what is f(9)?  [#permalink]

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18 Apr 2018, 10:26
anwer is C car a square root can never be negative
Re: If f(x)=√(x^2−2x+1), what is f(9)? &nbs [#permalink] 18 Apr 2018, 10:26
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