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

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

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New post Updated on: 21 Jun 2013, 02:29
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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, 10:45.
Last edited by Bunuel on 21 Jun 2013, 02:29, edited 2 times in total.
Edited the stem.
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Re: DS-Function  [#permalink]

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New post 22 Jul 2010, 11:13
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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.

Answer: B.

Hope it's clear.
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Re: DS-Function  [#permalink]

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New post 22 Jul 2010, 11:18
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.

Answer: B.

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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New post 10 Nov 2018, 23:48
RenukaD wrote:
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.

B is my answer.
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Re: For all integers n, the function f is defined by f (n) =   [#permalink] 10 Nov 2018, 23:48
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