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# The function f(x) is defined as f(x) = 1/(x + 1), where x is not equal

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The function f(x) is defined as f(x) = 1/(x + 1), where x is not equal  [#permalink]

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Updated on: 25 Sep 2018, 23:34
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Difficulty:

65% (hard)

Question Stats:

50% (02:51) correct 50% (02:30) wrong based on 14 sessions

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The function f(x) is defined as $$f(x)=\frac{1}{x+1}$$, where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a?

(I) f(a − 1) = f(a) – f(1)

(II) $$\frac{2}{f(a−1)}=\frac{2}{f(a)}−\frac{1}{f(1)}$$

(III) f(a − 1) = f(a)∗f(1)

(A) I only
(B) II only
(C) III only
(D) I, II and III
(E) None of the above

Originally posted by Probus on 25 Sep 2018, 21:00.
Last edited by Bunuel on 25 Sep 2018, 23:34, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Aug 2009
Posts: 6985
The function f(x) is defined as f(x) = 1/(x + 1), where x is not equal  [#permalink]

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25 Sep 2018, 23:32
Probus wrote:
The function f(x) is defined as f(x)=$$\frac{1}{x+1}$$, where x is not equal to -1. If a is not equal to -1 or 0, which of the following expressions must be true for all values of a?

(I) f(a−1)=f(a)–f(1)

(II)$$\frac{2}{f(a−1)}=\frac{2}{f(a)}−\frac{1}{f(1)}$$

(III)f(a−1)=f(a)∗f(1)

(A)I only

(B)II only

(C) III only

(D) I, II and III

(E)None of the above

Let us find value of f(a), f(1) and f(a-1) if a=3
So
1) $$f(1) = \frac{1}{(1+1)}=\frac{1}{2}$$
2) $$f(a)=f(3)=\frac{1}{(3+1)}=\frac{1}{4}$$
3) $$f(a-1)=f(3-1)=f(2)=\frac{1}{(2+1)}=\frac{1}{3}$$

Let us see the choices

(I) f(a−1)=f(a)–f(1)
So $$\frac{1}{3}=\frac{(1}{4})-\frac{1}{2}$$....NO

(II)$$\frac{2}{f(a−1)}=\frac{2}{f(a)}−\frac{1}{f(1)}$$
$$2/(\frac{1}{3})=2/(\frac{1}{4})-1/(\frac{1}{2}).....2*3=2*4-1*2.....6=8-2$$... YES

(III)f(a−1)=f(a)∗f(1)
$$\frac{1}{3}=\frac{1}{4}*1\frac{}{2}.$$....NO

Only II

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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The function f(x) is defined as f(x) = 1/(x + 1), where x is not equal &nbs [#permalink] 25 Sep 2018, 23:32
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