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If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x)

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If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x) [#permalink]

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If \(f(x) = \frac{343}{x^3}\), what is the value of \(f(7x)* f(\frac{x}{7})\) in terms of f(x)?


(A) \(f(x^2)\)

(B) \((f(x))^2\)

(C) \(f(x^3)\)

(D) \((f(x))^3\)

(E) \(f(343x)\)


Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x) [#permalink]

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New post 06 Apr 2015, 07:37
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Bunuel wrote:
If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x)?

(A) f(x^2)
(B) (f(x))^2
(C) f(x^3)
(D) (f(x))^3
(E) f(343x)


Kudos for a correct solution.


Firstly we should calculate result of f(7x)* f(x/7)

\(\frac{343}{(7x)^3}*\frac{343}{(x^3/7^3)} = \frac{343^2}{x^6}\)

After this calculations we see that this is result of formula raised to second power

And answer is B
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Re: If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x) [#permalink]

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New post 06 Apr 2015, 11:44
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Bunuel wrote:
If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x)?

(A) f(x^2)
(B) (f(x))^2
(C) f(x^3)
(D) (f(x))^3
(E) f(343x)


Kudos for a correct solution.


f(x) = 343/x^3
@x=7, f(7) = 343/7^3 = 1
@x=1, f(1) = 343/1^3 = 343
@x=49, f(49) = 343/49^3 = 1/343


Now f(7x)* f(x/7)
@x=7, f(7x)* f(x/7) = f(49)* f(1) = (1/343) x (343) = 1 = f(7) = [f(7)]^2 = [f(x)]^2

Answer: Option
[Reveal] Spoiler:
B

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Re: If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x) [#permalink]

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New post 06 Apr 2015, 15:06
Lets look at the function f(x) from a general point of view:
\(f(a*x) = \frac{343}{(a*x)^3} = \frac{1}{a^3}*\frac{343}{x^3} = \frac{1}{a^3}*f(x)\)
Now lets look at our question: F(7*x)*F(x/7). 7*x and x/7 contain reciprocal numbers 1/7 and 7, which will be reduced because \(\frac{7^3}{7^3} = 1\), leaving us with just a product of f(x) and f(x) thus leaving us with a f(x)^2 which matches option B.

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Re: If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x) [#permalink]

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New post 13 Apr 2015, 07:55
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Bunuel wrote:
If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x)?

(A) f(x^2)
(B) (f(x))^2
(C) f(x^3)
(D) (f(x))^3
(E) f(343x)


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

to get f(a) given f(x), all you need to do is substitute x with a.

f(x) = 343/x^3

f(7x) = 343/(7x)^3 = 1/x^3

f(x/7) = 343/(x/7)^3 = 343*343/x^3

So we get f(7x) * f(x/7) = (1/x^3) * (343*343/x^3) = (343/x^3)^2

But we know that 343/x^3 = f(x)

So, f(7x) * f(x/7) = (f(x))^2

Answer(B)

There are other ways of solving this too:

Say x = 1, then f(1) = 343

f(7x)* f(x/7) = f(7)*f(1/7) = (343/7^3) * (343/(1/7)^3 = (343)^2

So f(7x)* f(x/7) = (f(1))^2
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Re: If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x) [#permalink]

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New post 29 Sep 2017, 10:19
Bunuel wrote:
If \(f(x) = \frac{343}{x^3}\), what is the value of \(f(7x)* f(\frac{x}{7})\) in terms of f(x)?


(A) \(f(x^2)\)

(B) \((f(x))^2\)

(C) \(f(x^3)\)

(D) \((f(x))^3\)

(E) \(f(343x)\)


Kudos for a correct solution.


Notice that 343 = 7^3, so we can write f(x) = 343/x^3 as f(x) = 7^3/x^3 = (7/x)^3. Furthermore:

f(7x) = (7/(7x))^3 = (1/x)^3 = 1/x^3

and

f(x/7) = (7/(x/7))^3 = (49/x)^3 = 49^3/x^3.

So, f(7x) * f(x/7) = 1/x^3 * 49^3/x^3 = 49^3/x^6.

Notice that 49 = 7^2, so 49^3/x^6 = (7^2)^3/x^6 = 7^6/x^6 = (7/x)^6 = ((7/x)^3)^2. Since f(x) = (7/x)^3, ((7/x)^3)^2 = (f(x))^2.

Answer: B
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Re: If f(x) = 343/x^3, what is the value of f(7x)* f(x/7) in terms of f(x)   [#permalink] 29 Sep 2017, 10:19
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