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If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:

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Bunuel
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If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink] New post   05 Nov 2014, 08:38
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Tough and Tricky questions: Algebra.



If \(f(x) = ax^4 – 4x^2 + ax – 3\), then \(f(b) – f(-b)\) will equal:


A. 0

B. \(2ab\)

C. \(2ab^4 – 8b^2 – 6\)

D. \(-2ab^4 + 8b^2 + 6\)

E. \(2ab^4 – 8b^2 + 2ab – 6\)


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B
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manpreetsingh86
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink] New post   06 Nov 2014, 01:58
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Bunuel wrote:

Tough and Tricky questions: Algebra.



If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:

A. 0
B. 2ab
C. 2ab^4 – 8b^2 – 6
D. -2ab^4 + 8b^2 + 6
E. 2ab^4 – 8b^2 + 2ab – 6

Kudos for a correct solution.


f(b)= ab^4 – 4b^2 + ab – 3 ----------------- 1)
f(-b)= ab^4 – 4b^2 - ab – 3 -------------------2)

1-2, will give us f(b)-f(-b)= 2ab
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink] New post   06 Nov 2014, 19:58
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Bunuel wrote:

Tough and Tricky questions: Algebra.



If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal:

A. 0
B. 2ab
C. 2ab^4 – 8b^2 – 6
D. -2ab^4 + 8b^2 + 6
E. 2ab^4 – 8b^2 + 2ab – 6

Kudos for a correct solution.



\(f(x) = ax^4 - 4x^2 + ax - 3\)

\(f(b) = ab^4 - 4b^2 + ab - 3\)

\(f(-b) = a(-b)^4 - 4(-b)^2 + a(-b) - 3\)
\(f(-b) = ab^4 - 4b^2 - ab - 3\)

\(f(b) - f(-b) = [ab^4 - 4b^2 + ab - 3] - [ab^4 - 4b^2 - ab - 3]\)
\(f(b) - f(-b) = ab^4 - 4b^2 + ab- 3 - ab^4 + 4b^2+ ab + 3\)
\(f(b) - f(-b) = ab + ab\)
\(f(b) - f(-b) = 2ab\)

Answer is B
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink] New post   06 Nov 2014, 15:29
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Bunuel wrote:

Tough and Tricky questions: Algebra.



If f(x)=ax^4–4x^2+ax–3, then f(b) – f(-b) will equal:

A. 0
B. 2ab
C. 2ab^4 – 8b^2 – 6
D. -2ab^4 + 8b^2 + 6
E. 2ab^4 – 8b^2 + 2ab – 6

Kudos for a correct solution.



f(x)=ax^4 – 4x^2 + ax – 3

f(b) = ab^4 – 4b^2 + ab – 3
f(-b) = ab^4 – 4b^2 - ab – 3

f(b) - f(-b) = ab^4 – 4b^2 + ab – 3 - ab^4 + 4b^2 + ab + 3
=2ab

Answer B
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink] New post   10 Nov 2014, 00:16
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\(f(x) = ax^4 – 4x^2 + ax – 3\)

For all even powers, sign would remain the same. For all odd powers, sign would change

\(f(b) - f(-b) = ab^4 - 4b^2 + ab - 3 - (ab^4 - 4b^2 - ab - 3) = 2ab\)

Answer = B
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink] New post   08 Feb 2018, 08:18
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Substitue the b with any negative number and make that number to the power of 4 and solve for it. You will get a positive figure, as any number to the power of even number will result a positive figure


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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink] New post   08 Feb 2018, 07:37
I do not understand why does a(-b)^4 become ab^4 ??
it has to be -ab^4, doesn't it ?
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink] New post   09 Feb 2018, 17:56
If you look at just -3 then

-3 - (-3) = 0

C, D, and E are out

From there, you can solve until you realize it does not = 0



Bunuel wrote:

Tough and Tricky questions: Algebra.



If \(f(x) = ax^4 – 4x^2 + ax – 3\), then \(f(b) – f(-b)\) will equal:


A. 0

B. \(2ab\)

C. \(2ab^4 – 8b^2 – 6\)

D. \(-2ab^4 + 8b^2 + 6\)

E. \(2ab^4 – 8b^2 + 2ab – 6\)


Kudos for a correct solution.
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Re: If f(x) = ax^4 – 4x^2 + ax – 3, then f(b) – f(-b) will equal: [#permalink] New post   11 Feb 2018, 01:43
gmatmo wrote:
I do not understand why does a(-b)^4 become ab^4 ??
it has to be -ab^4, doesn't it ?


hi gmatmo

\((-b)^4=-b*-b*-b*-b\).

In your opinion what should be the result of this multiplication?
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If f(x) = ax^4 4x^2 + ax 3, then f(b) f(-b) will equal: [#permalink] New post   07 Aug 2022, 10:51
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Given that \(f(x) = ax^4 – 4x^2 + ax – 3\) and we need to find the value of f(b) – f(–b)

To find f(b) we need to compare what is inside the bracket in f(b) and f(x)

=> We need to substitute x with b in \(f(x) = ax^4 – 4x^2 + ax – 3\) to get the value of f(b)
=> \(f(b) = ab^4 – 4b^2 + a*b – 3\) = \(ab^4 – 4b^2 + ab – 3\)

Similarly, \(f(-b) = a(-b)^4 – 4(-b)^2 + a*(-b) – 3\) = \(ab^4 – 4b^2 - ab – 3\)
=> f(b) - f(-b) = \(ab^4 – 4b^2 + ab – 3\) - (\(ab^4 – 4b^2 - ab – 3\))
= \(ab^4 - ab^4 – 4b^2 + 4b^2 + ab + ab – 3 + 3\) = 2ab

So, Answer will be B
Hope it helps!

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If f(x) = ax^4 4x^2 + ax 3, then f(b) f(-b) will equal: [#permalink]
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