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# For all integers i, f(i) = i(i-1). What is the value of f(x)?

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For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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03 Aug 2018, 09:12
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85% (hard)

Question Stats:

42% (02:04) correct 58% (01:57) wrong based on 76 sessions

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For all integers i, f(i) = i(i-1). What is the value of f(x)?

(1) f(x)=x
(2) f(x-1) = (x-2)

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Re: For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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03 Aug 2018, 10:09
For all integers i, f(i) = i(i-1). What is the value of f(x)?

(1) f(x)=x.

f(x) = x(x - 1), so x(x - 1) = x --> x = 0 or x = 2.

If x = 0, then f(x) = 0 but if x = 2, then f(x) = 2. Not sufficient.

(2) f(x-1) = (x-2).

f(x - 1) = (x - 1)(x - 1 - 1), so (x - 1)(x - 1 - 1) = (x - 2) --> x = 2.

If x = 2, then f(x) = f(2) = 2(2 - 1) = 2. Sufficient.

Hope it's clear.
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Re: For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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06 Aug 2018, 13:03
Bunuel wrote:
For all integers i, f(i) = i(i-1). What is the value of f(x)?

(1) f(x)=x.

f(x) = x(x - 1), so x(x - 1) = x --> x = 0 or x = 2.

If x = 0, then f(x) = 0 but if x = 2, then f(x) = 2. Not sufficient.

(2) f(x-1) = (x-2).

f(x - 1) = (x - 1)(x - 1 - 1), so (x - 1)(x - 1 - 1) = (x - 2) --> x = 2.

If x = 2, then f(x) = f(2) = 2(2 - 1) = 2. Sufficient.

Hope it's clear.

for statement 1 , I did x(x-1)=x, so x^2-x=x => x^2=2x =>x=2 .... i am not able to understand how x can be 0 going by this
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Re: For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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06 Aug 2018, 13:11
Bunuel wrote:
For all integers i, f(i) = i(i-1). What is the value of f(x)?

(1) f(x)=x.

f(x) = x(x - 1), so x(x - 1) = x --> x = 0 or x = 2.

If x = 0, then f(x) = 0 but if x = 2, then f(x) = 2. Not sufficient.

(2) f(x-1) = (x-2).

f(x - 1) = (x - 1)(x - 1 - 1), so (x - 1)(x - 1 - 1) = (x - 2) --> x = 2.

If x = 2, then f(x) = f(2) = 2(2 - 1) = 2. Sufficient.

Hope it's clear.

for statement 1 , I did x(x-1)=x, so x^2-x=x => x^2=2x =>x=2 .... i am not able to understand how x can be 0 going by this

$$x^2=2x$$
Or, $$x^2-2x=0$$
Or, x(x-2)=0
Or, x=0 or x-2=0

So, x=0, 2

P.S.:- When you see variables in both sides of linear equations or inequalities, never cancel the common variable terms instead drag them to one side and factorize.
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For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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06 Aug 2018, 13:25

x^2=2x => x^2-2x=0 => x(x-2)=0 => x=0 OR (x-2)=0 => x=0 OR x=2
For all integers i, f(i) = i(i-1). What is the value of f(x)?   [#permalink] 06 Aug 2018, 13:25
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