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If the function f is defined for all x by f(x)= ax^2+bx-43, where a an

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If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink] New post   Updated on: 18 Dec 2014, 10:11
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If the function f is defined for all x by f(x)= ax^2+bx-43, where a and b are constants, what is the value of f(3)?

(1) f(4)=41
(2) 3a +b=17

My question is statement 1 gives a linear equation and so does the question stem? why isn't it sufficient?
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Originally posted by Gmatdecoder on 18 Dec 2014, 09:31.
Last edited by Bunuel on 18 Dec 2014, 10:11, edited 1 time in total.
RENAMED THE TOPIC.
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Re: If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink] New post   18 Dec 2014, 10:22
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If the function f is defined for all x by f(x)= ax^2+bx-43, where a and b are constants, what is the value of f(3)?

We want the value of f(3), which is 9a + 3b - 43

(1) f(4)=41. This implies that 16a + 4b- 43 = 41. Fromthis we cannot get the value of 9a + 3b - 43. Not sufficient.

(2) 3a +b=17 --> multiply by 3: 9a + 3b = 51, therefore 9a + 3b - 43 = 51 - 43 = 8. Sufficient.

Answer: B.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rule 3. Thank you.

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Re: If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink] New post   18 Dec 2014, 10:23
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Gmatdecoder wrote:
If the function f is defined for all x by f(x)= ax^2+bx-43, where a and b are constants, what is the value of f(3)?

(1) f(4)=41
(2) 3a +b=17

My question is statement 1 gives a linear equation and so does the question stem? why isn't it sufficient?


Check function questions in our Special Questions Directory:

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
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Re: If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink] New post   18 Dec 2014, 23:57
sorry for ignorance of forum rules.

Thanks for the explanation.

I have trouble interpreting the first statement. The first statement and equation in the question can be used to find values of a, and b by solving. Inputting a, b in the question and x=3 finds value for f(3). what am i missing here?
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Re: If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink] New post   19 Dec 2014, 08:35
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Gmatdecoder wrote:
sorry for ignorance of forum rules.

Thanks for the explanation.

I have trouble interpreting the first statement. The first statement and equation in the question can be used to find values of a, and b by solving. Inputting a, b in the question and x=3 finds value for f(3). what am i missing here?


Which two equations give the value of 9a + 3b - 43?

For (1) we have only one equation: 16a + 4b- 43 = 41 (from f(x)= ax^2+bx-43). We don't have any other equation with a and b to solve for them.

Does this make sense?
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Re: If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink] New post   20 Dec 2014, 00:12
Thanks..

I was treating them as simultaneous equations.
9a + 3b=43--------------(I) from question stem
16a + 4b=84-------------(II) from statement I

and solving for a and b (constants) then inputting in the question stem with x=(3), but i guess these are statements for values of functions where in f(3) cannot be equated to f(4).

Is that logic right?
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Re: If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink] New post   20 Dec 2014, 08:22
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Gmatdecoder wrote:
Thanks..

I was treating them as simultaneous equations.
9a + 3b=43--------------(I) from question stem
16a + 4b=84-------------(II) from statement I

and solving for a and b (constants) then inputting in the question stem with x=(3), but i guess these are statements for values of functions where in f(3) cannot be equated to f(4).

Is that logic right?


We are NOT given that 9a + 3b = 43. The question asks to find the value of 9a + 3b - 43.
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Re: If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink] New post   20 Dec 2014, 23:53
Thanks that clears my misunderstanding...
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Re: If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink] New post   14 Mar 2024, 08:36
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Re: If the function f is defined for all x by f(x)= ax^2+bx-43, where a an [#permalink]
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