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If g(x) = ax^5 + bx^3 + 1, and g(5) = 10, then g(–5) =?

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If g(x) = ax^5 + bx^3 + 1, and g(5) = 10, then g(–5) =?  [#permalink]

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New post Updated on: 19 Aug 2013, 11:52
1
5
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:34) correct 25% (01:58) wrong based on 374 sessions

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If g(x) = ax^5 + bx^3 + 1, and g(5) = 10, then g(–5) =?

(A) – 10
(B) – 8
(C) – 6
(D) 0
(E) 4

Originally posted by galiya on 19 Aug 2013, 11:38.
Last edited by Bunuel on 19 Aug 2013, 11:52, edited 1 time in total.
Edited the question and added the OA
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Re: If g(x) = ax5 + bx3 + 1  [#permalink]

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New post 19 Aug 2013, 11:51
1
4
Galiya wrote:
If g(x) = ax5 + bx3 + 1, and g(5) = 10, then g(–5) =?



(A) – 10
(B) – 8
(C) – 6
(D) 0
(E) 4


given:
\(g(5) = 10\)
therefore
\(a*5^5 + b5^3 + 1 = 10\)
\(a*5^5 + b5^3 = 9\) ..................................(1
\(g(-5) = -a*5^5 - b5^3 + 1\)
\(=- (a*5^5 + b5^3)+1\)
now using 1
\(g(-5) = -9 + 1 = -8\)

hence B
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Re: If g(x) = ax^5 + bx^3 + 1, and g(5) = 10, then g(–5) =?  [#permalink]

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New post 19 Aug 2013, 13:39
1
Galiya wrote:
If g(x) = ax^5 + bx^3 + 1, and g(5) = 10, then g(–5) =?

(A) – 10
(B) – 8
(C) – 6
(D) 0
(E) 4


g(5) = 10
or, 5^5 a + 5^3 b + 1 = 10
or, 5^5 a + 5^3 b = 9

g(-5) = -5^5 a - 5^3 b + 1 = - (5^5 a + 5^3 b) + 1 = - 9 + 1 = - 8 = (B)
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If g(x) = ax^5 + bx^3 + 1, and g(5) = 10, then g(–5) =?  [#permalink]

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New post 04 Aug 2016, 22:24
Galiya wrote:
If \(g(x) = ax^5 + bx^3 + 1\), and \(g(5) = 10\), then \(g(–5) =?\)


When raising a number to an odd power, if we negate the number, we negate the sign of the result.

\(ax^5 + bx^3 = 9 \, (x:5)\\
ax^5 + bx^3 = -9 \, (x:-5)\)

\(-9 + 1 = -8\)

(B) – 8

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Re: If g(x) = ax^5 + bx^3 + 1, and g(5) = 10, then g(–5) =?  [#permalink]

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New post 07 Apr 2017, 15:23
it look me almost 3 minutes to solve it...
first:
g(5) = a*5^5 + b*5^3 +1 = 10
a*5^5 + b*5^3 = 9
5^3 * (a*5^2 + b) = 9
125 * (25a + b) = 9
25a + b = 9/125


now
g(-5) = a*-5^5 + b*-5^3 +1
we can factor out -5^3
-5^3 * (a*-5^2 +b) +1
-125*(25a + b) +1

we know 25a + b = 9/125
-125* 25a + b = -9
125*(25a + b) +1 = -8

answer is B.
Re: If g(x) = ax^5 + bx^3 + 1, and g(5) = 10, then g(–5) =? &nbs [#permalink] 07 Apr 2017, 15:23
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