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Intern  Joined: 02 Feb 2014
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what is the greatest possible value of the function f(x)?  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 38% (01:21) correct 62% (01:18) wrong based on 87 sessions

HideShow timer Statistics what is the greatest possible value of the function f(x)?

(1) f(x)=k-x^2

(2) the straightline distance between the two roots of f(x) is 6.

Originally posted by venkateshreddy on 07 Apr 2014, 03:47.
Last edited by abhimahna on 04 Jul 2018, 05:34, edited 2 times in total.
Edited the question and added OA
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Re: what is the greatest possible value of the function f(x)?  [#permalink]

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slemtem wrote:
(1) If x^2 = 0, f(x)=k. This is the largest value as x^2 can't be negative. SUFFICIENT.

(A)

In GMAT, until you get a singular numerical value, that statement is not sufficient.

From F.S 1, we know that $$f(x) = k-x^2$$ . Now, the largest value of f(x) would be at x=0, however, that value would be 'k' and this is not a numerical value. Insufficient.

From F.S 2, we know that the difference between the roots of f(x) is 6. The is clearly Insufficient.

Taking both together, we know that for y=0, we have $$x^2= k$$ and the roots are = $$\pm\sqrt{k}.$$

Also, $$|\sqrt{k}-(-\sqrt{k})| = 6$$ -->$$2\sqrt{k}$$= 6. We know the value of 'k'. Sufficient.

C.
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Re: what is the greatest possible value of the function f(x)?  [#permalink]

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(1) If x^2 = 0, f(x)=k. This is the largest value as x^2 can't be negative. SUFFICIENT.

(A)
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Re: what is the greatest possible value of the function f(x)?  [#permalink]

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Question asks - do we have enough information to calculate maximum value of some function.

1) we don't know what k is therefore we cannot know the value of f(x) (INS)
2) we do not know what f(x) is so distance between roots is meaningless. (INS)

1+2) knowing that $$f(x)= -x^2 + k$$, we know that equation has 2 roots.
we can rewrite the function as: $$(\sqrt{k}+x)(\sqrt{k}-x)=0$$
$$x=\sqrt{k}$$ or $$x=-\sqrt{k}$$
in order to achieve distance of 6, each root's absolute value needs to be 3. 6/2=3. So our roots are 3 and -3 on a parabola and k=9
Knowing k we can calculate $$f(x)=-x^2+9$$

Sufficient: C
Attachments x2+k.png [ 6.3 KiB | Viewed 4910 times ]

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Re: what is the greatest possible value of the function f(x)?  [#permalink]

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venkateshreddy wrote:
what is the greatest possible value of the function f(x)?

(1) f(x)=k-x^2

(2) the straightline distance between the two roots of f(x) is 6.

THE OA IS NOT PROVIDED

We have to find the max possible value for the function. which is possible when x= 0 or x^2= 0

but we have found the value of x = 3 and -3 and corresponding value of k = 9

shouldn't we have found the value of K when x= 0 to show the max value of the function?

This is a different kind of sum which I am not able to fully comprehend? also here, is f(x) the equation of a parabola?

Can some one more clarify this for me.
Thank you
Intern  Joined: 13 Jun 2014
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GMAT 1: 660 Q48 V33 Re: what is the greatest possible value of the function f(x)?  [#permalink]

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qlx wrote:
venkateshreddy wrote:
what is the greatest possible value of the function f(x)?

(1) f(x)=k-x^2

(2) the straightline distance between the two roots of f(x) is 6.

THE OA IS NOT PROVIDED

We have to find the max possible value for the function. which is possible when x= 0 or x^2= 0

but we have found the value of x = 3 and -3 and corresponding value of k = 9

shouldn't we have found the value of K when x= 0 to show the max value of the function?

This is a different kind of sum which I am not able to fully comprehend? also here, is f(x) the equation of a parabola?

Can some one more clarify this for me.
Thank you

Yes QLX ... Your approach is correct. In your approach also you are getting option C as correct which is indeed the right answer.

You are also correct when you say that it the equation of the parabola.

Parabola eq: f(x)=y=a(x^2) + bx + c

Comparing it with f(x)=k-x^2 :

We get 'b' is zero. And since 'a' is negative , we get a parabola that opens downward.

In a parabola equation, to get x-intercepts(i.e roots) , put y=0. And we get +/- sq. root of k ---> So the parabola cuts the x axis at two places.
The distance between these roots is mentioned as 6. So sq. root of k= 3.. Then k=9.

Now the point on y axis where x =0 will be the maximum value for the function. i.e. y=k .. Hence y=9 is maximum value.

This is the method to solve through parabola.

You just solved it in a different way, but yours is also correct
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Re: what is the greatest possible value of the function f(x)?  [#permalink]

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_________________ Re: what is the greatest possible value of the function f(x)?   [#permalink] 10 Sep 2018, 09:47
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