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carcass
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The function f is defined by f(x) = ax^4 28 Aug 2023, 11:20
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76% (01:26) correct 24% (02:19) wrong based on 142 sessions

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The function f is defined by \(f(x) = ax^4 – 4x^2 + ax – 3\) for all numbers x. What will \(f(b) – f(–b)\) equal?

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


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B
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The function f is defined by f(x) = ax^4 28 Aug 2023, 11:46
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f(b)= ab^4-4b^2+ab-3
f(-b)= ab^4-4b^2-ab-3
f(b)-f(-b)= ab^4-ab^4-4b^2+4b^2+ab+ab-3+3
= 2ab
Option B is the answer

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The function f is defined by f(x) = ax^4 28 Aug 2023, 12:35
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The function f is defined by \(f(x) = ax^4 – 4x^2 + ax – 3\) for all numbers x. What will \(f(b) – f(–b)\) equal?

A. 0
B. \(2ab\)
C. \(–8b^2 – 6\)
D. \(2ab^4 –8b^2 – 6\)
E. \(2ab^4 –8b^2 + 2ab – 6\)
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Assume :

  • b = 1
  • -b = -1

f(b) = a - 4 + a - 3 = 2a - 7

f(-b) = a - 4 - a - 3 = - 7

f(b) - f(-b) = 2a - 7 + 7 = 2a

Answer choice elimination

A. 0 → Eliminate

B. \(2ab\) → 2a

Matches with expected answer → Keep

C. \(–8b^2 – 6\) → Eliminate as the value is independent of a

D. \(2ab^4 –8b^2 – 6\)→ \(2a - 8 - 6 = 2a - 14\)

Eliminate

E. \(2ab^4 –8b^2 + 2ab – 6\) → \(2a - 8 + 2a - 6 = 4a - 14\)

Eliminate

Option B
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The function f is defined by f(x) = ax^4 18 Nov 2023, 02:34
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\(f(x) = ax^4 – 4x^2 + ax – 3\) and we need to find the value of \(f(b) – f(–b)\)

Now, f(b) and f(-b) will have same terms but
    - Terms with even power of b will have same sign
    - Terms with odd power of b will have different sign
    - Constant terms with no power of b will have same sign

So, if we are finding the value of f(b) - f(-b) then the terms with same sign will cancel out and we will be left with terms with different signs only

=> f(b) - f(-b) = ab - (a*-b) = 2ab

Detailed step by step solution

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

So, Answer will be B
Hope it helps!

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