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

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Senior Manager
Joined: 18 Feb 2019
Posts: 386
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
The function f(x) is defined as f(x)=1/(x+1), where x is not equal to  [#permalink]

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10 Apr 2019, 11:17
00:00

Difficulty:

55% (hard)

Question Stats:

60% (02:04) correct 40% (02:37) wrong based on 20 sessions

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The function f(x) is defined as f(x)=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. 2/f(a−1)=2/f(a)−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
Manager
Joined: 12 Sep 2017
Posts: 247
The function f(x) is defined as f(x)=1/(x+1), where x is not equal to  [#permalink]

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12 Apr 2019, 13:50
$$\frac{2}{(1/((a-1)+1)))}$$ = $$\frac{2}{(1/(a+1))}$$ - $$\frac{1}{(1/2)}$$

$$\frac{2}{(1/a)}$$ = $$2(a+1) - 2$$

$$2a = 2a + 2 - 2$$

$$2a = 2a$$

B
The function f(x) is defined as f(x)=1/(x+1), where x is not equal to   [#permalink] 12 Apr 2019, 13:50
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