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# For all integers n, the function f is defined by f (n) =

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Manager
Joined: 24 Jan 2010
Posts: 90
Location: India
Schools: ISB
For all integers n, the function f is defined by f (n) =  [#permalink]

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Updated on: 21 Jun 2013, 01:29
4
00:00

Difficulty:

15% (low)

Question Stats:

72% (00:46) correct 28% (00:46) wrong based on 247 sessions

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For all integers n, the function f is defined by f (n) = a^n, where a is a constant. What is the value of f (1)?

(1) f (2) = 100
(2) f (3) = -1,000

Originally posted by RenukaD on 22 Jul 2010, 09:45.
Last edited by Bunuel on 21 Jun 2013, 01:29, edited 2 times in total.
Edited the stem.
Math Expert
Joined: 02 Sep 2009
Posts: 50627

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22 Jul 2010, 10:13
2
Edited the stem. It should be:

For all integers n, the function f is defined by f (n) = a^n, where a is a constant. What is the value of f (1)?

$$f(1)=a^1=a$$, so basically the question is: what is the value of $$a$$?

(1) f(2) = 100 --> $$f(2)=100=a^2$$ --> $$a=10$$ or $$a=-10$$. Two answers, not sufficient.

(2) f(3) = -1,000 --> --> $$f(3)=-1,000=a^3$$ --> only one solution: $$a=-10$$. Sufficient.

Hope it's clear.
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Joined: 24 Jan 2010
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22 Jul 2010, 10:18
1
Bunuel wrote:
Edited the stem. It should be:

For all integers n, the function f is defined by f (n) = a^n, where a is a constant. What is the value of f (1)?

$$f(1)=a^1=a$$, so basically the question is: what is the value of $$a$$?

(1) f(2) = 100 --> $$f(2)=100=a^2$$ --> $$a=10$$ or $$a=-10$$. Two answers, not sufficient.

(2) f(3) = -1,000 --> --> $$f(3)=-1,000=a^3$$ --> only one solution: $$a=-10$$. Sufficient.

Hope it's clear.

I apologize Bunuel for mistake in stem

Thanks a ton for correcting the mistake and the solution.

You really explain things very well
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Re: For all integers n, the function f is defined by f (n) =  [#permalink]

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10 Nov 2018, 22:48
For all integers n, the function f is defined by f (n) = a^n, where a is a constant. What is the value of f (1)?

(1) f (2) = 100
(2) f (3) = -1,000

f(1) = a^1. So we need to find the value of a.

Statement 1: f(2) = a^2 = 100. a can be 10 or -10.
Insufficient.

Statement 2: f(3) = a^3 = 1000. a = 10.
Sufficient.

Re: For all integers n, the function f is defined by f (n) = &nbs [#permalink] 10 Nov 2018, 22:48
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