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

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03 Jul 2017, 02:02
2
15
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Difficulty:

65% (hard)

Question Stats:

58% (02:17) correct 42% (02:14) wrong based on 159 sessions

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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

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

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03 Jul 2017, 02:06
2
2
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

@x=1, 3f(1) + 2f(-1) = 5 − 10 = -5

@x=-1, 3f(-1) + 2f(1) = -5 − 10 = -15

Multiply the equation 1 with 3 and equation 2 with 2 and subtract

5*f(1) = -15+30 = 15

f(1) = 3

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

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03 Jul 2017, 03:18
2
If x=1, 3f(1) + 2f(-1) = 5 − 10 = -5
If x=-1, 3f(-1) + 2f(1) = -5 − 10 = -15

Let f(1) = a and f(-1) = b
Now, the equations become :
3a + 2b = -5
2a + 3b = -15
Since we have been asked to find the value of f(1) or a, we have to eliminate f(-1) or b

Multiplying the first equation by 3 and subtracting from it the second equation(multiplied by 2)
3(3a + 2b) - 2(2a + 3b) = -15 + 30
9a - 4a = 15 -> 5a = 15 -> a(f(1)) =3 (Option 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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16 Jul 2017, 17:30
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 we let x = 1, we have 3f(1) + 2f(-1) = 5(1) - 10, i.e., 3f(1) + 2f(-1) = -5.

If we let x = -1, we have 3f(-1) + 2f(-(-1)) = 5(-1) - 10, i.e., 3f(-1) + 2f(1) = -15.

Now we need to “get rid” of f(-1) to find the value of f(1). To do that, we multiply the first equation by 3 and the second equation by 2:

3 x [3f(1) + 2f(-1) = -5] → 9f(1) + 6f(-1) = -15

2 x [3f(-1) + 2f(1) = -15] → 6f(-1) + 4f(1) = -30

Now if we subtract 6f(-1) + 4f(1) = -30 from 9f(1) + 6f(-1) = -15, we have:

5f(1) = 15

f(1) = 3

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

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15 Oct 2018, 07:16
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Re: If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?   [#permalink] 15 Oct 2018, 07:16
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