If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)? : Problem Solving (PS)

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If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)?

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Joined: 02 Sep 2009

Posts: 49992

If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)? [#permalink]

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01 Oct 2018, 23:14

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If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Spoiler: OA

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Re: If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)? [#permalink]

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01 Oct 2018, 23:24

Bunuel wrote:

If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

3f(x) + 2f(−x) = 5x − 10
2f(x) + 3f(-x) = -5x - 10

9f(x) + 6f(-x) = 15x - 30
4f(x) + 6f(-x) = -10x - 20

Subtract the above two equation -

5f(x) = 25x - 10
f(x) = 5x - 2
f(1) = 3

Hence, D.
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Re: If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)? [#permalink]

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01 Oct 2018, 23:50

Bunuel wrote:

If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

If \(x=1\), the equation becomes \(3f(1) + 2f(-1) = 5 - 10 = -5\) -> (1)

If \(x=-1\), the equation becomes \(3f(-1) + 2f(1) = -5 - 10 = -15\) -> (2)

3*(1) - 2*(2) -> \(9f(1) - 4f(1) = -15 + 30 = 15\) -> \(5f(1) = 15\)

Therefore, the value of f(1) = \(\frac{15}{5}\) = 3(Option D)
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