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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms Updated on: 18 Jul 2013, 22:26
Originally posted by manulath on 24 Aug 2012, 05:04.
Last edited by Bunuel on 18 Jul 2013, 22:26, edited 2 times in total.
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If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(\frac{x}{5})\) in terms of f(x)?

A. \((f(x))^{2}\)

B. \(f(x^{2})\)

C. \((f(x))^{3}\)

D. \(f(x^{3})\)

E. \(f(125x)\)
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A
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 24 Aug 2012, 05:58
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If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(\frac{f(5x)}{f(x/5)}\) in terms of f(x)?

A. \((f(x))^{2}\)

B. \(f(x^{2})\)

C. \((f(x))^{3}\)

D. \(f(x^{3})\)

E. \(f(125x)\)
Show more

In order the answer to be A, the question should read:

If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(x/5)\) in terms of f(x)?

Say \(x=1\), then:

\(f(x) = f(1)=\frac{125}{1^{3}}=125\);

\(f(5x)=f(5)=\frac{125}{5^3}=1\);

\(f(\frac{x}{5})=f(\frac{1}{5})=\frac{125}{(\frac{1}{5})^3}=125*125\).

\({f(5x)}*{f(\frac{x}{5})}={f(5)}*{f(\frac{1}{5})}=125^2\) and since \(f(x) = f(1)=125\), then \({f(5x)}*{f(\frac{x}{5})}=125^2=(f(x))^2\).

Answer: A.

Hope it's clear.
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 04 Jul 2013, 00:48
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If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(x/5)\) in terms of f(x)?

A. \((f(x))^{2}\)

B. \(f(x^{2})\)

C. \((f(x))^{3}\)

D. \(f(x^{3})\)

E. \(f(125x)\)
Show more

1. \(f(5x) = 125/125*x^3 = 1/x^3\)
2.\(f(x/5) = 125 * 125/x^3 = 125^2 / x^3\)
3. \(f(5x) * f(x/5) = 125 ^ 2/ x^6 = (f(x)) ^ {2}\)
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 24 Aug 2012, 06:05
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In order the answer to be A, the question should read:
If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(x/5)\) in terms of f(x)?

Show more

Thanks Bunuel.

The question really troubled me.
I tried methods and still could not arrive at correct answer.
Your verdict has confirmed my doubt.

I shall edit the question.

PS: You already did that. Thanks again.
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 03 Jul 2013, 01:23
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 03 Jul 2013, 08:44
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manulath
If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(x/5)\) in terms of f(x)?

A. \((f(x))^{2}\)

B. \(f(x^{2})\)

C. \((f(x))^{3}\)

D. \(f(x^{3})\)

E. \(f(125x)\)
Show more

lets 125 =A
so we can write f(x)=A/(X^3)...........(1
Now lets sove

f(5x)*f(x/5)=(A/(5X)^3)*(A/(X/5)^3)====>(A^2/X^6)===>(A/X^3)^2==(F(X))^2==>USING(1)

Hence A
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 18 Jul 2013, 18:30
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manulath
If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(x/5)\) in terms of f(x)?

A. \((f(x))^{2}\)

B. \(f(x^{2})\)

C. \((f(x))^{3}\)

D. \(f(x^{3})\)

E. \(f(125x)\)

1. \(f(5x) = 125/125*x^3 = 1/x^3\)
2.\(f(x/5) = 125 * 125/x^3 = 125^2 / x^3\)
3. \(f(5x) * f(x/5) = 125 ^ 2/ x^6 = (f(x)) ^ {2}\)
Show more

In step 3, you have multiplied 1. & 2. What would be the answer if you divide 1. by 2. ? I am kinda confused. I get f(5x)/f(x/5) = 1/5^6. Help, thanks!
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 18 Jul 2013, 22:26
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manulath
If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(x/5)\) in terms of f(x)?

A. \((f(x))^{2}\)

B. \(f(x^{2})\)

C. \((f(x))^{3}\)

D. \(f(x^{3})\)

E. \(f(125x)\)

1. \(f(5x) = 125/125*x^3 = 1/x^3\)
2.\(f(x/5) = 125 * 125/x^3 = 125^2 / x^3\)
3. \(f(5x) * f(x/5) = 125 ^ 2/ x^6 = (f(x)) ^ {2}\)

In step 3, you have multiplied 1. & 2. What would be the answer if you divide 1. by 2. ? I am kinda confused. I get f(5x)/f(x/5) = 1/5^6. Help, thanks!
Show more

The questions is "what is the value of \(f(5x)*f(\frac{x}{5})\)..." (f(5x) multiplied by f(x/5)) not "what is the value of \(\frac{f(5x)}{f(\frac{x}{5})}\)..." (f(5x) divided by f(x/5)).
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 18 Jul 2013, 22:47
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The questions is "what is the value of \(f(5x)*f(\frac{x}{5})\)..." (f(5x) multiplied by f(x/5)) not "what is the value of \(\frac{f(5x)}{f(\frac{x}{5})}\)..." (f(5x) divided by f(x/5)).
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Please refer your Ist response in this topic, the quoted part asks to find \(\frac{f(5x)}{f(\frac{x}{5})}\). Also, the question I have from my source of practice questions requires to find the \(\frac{f(5x)}{f(\frac{x}{5})}\). Thanks!
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 18 Jul 2013, 22:49
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The questions is "what is the value of \(f(5x)*f(\frac{x}{5})\)..." (f(5x) multiplied by f(x/5)) not "what is the value of \(\frac{f(5x)}{f(\frac{x}{5})}\)..." (f(5x) divided by f(x/5)).

Please refer your Ist response in this topic, the quoted part asks to find \(\frac{f(5x)}{f(\frac{x}{5})}\). Also, the question I have from my source of practice questions requires to find the \(\frac{f(5x)}{f(\frac{x}{5})}\). Thanks!
Show more

Please refer to the same post: in order the answer to be A, the question should read:
If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(\frac{x}{5})\) in terms of f(x)?
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 24 Aug 2013, 06:09
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manulath
If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(\frac{f(5x)}{f(x/5)}\) in terms of f(x)?

A. \((f(x))^{2}\)

B. \(f(x^{2})\)

C. \((f(x))^{3}\)

D. \(f(x^{3})\)

E. \(f(125x)\)

In order the answer to be A, the question should read:

If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(x/5)\) in terms of f(x)?

Say \(x=1\), then:

\(f(x) = f(1)=\frac{125}{1^{3}}=125\);

\(f(5x)=f(5)=\frac{125}{5^3}=1\);

\(f(\frac{x}{5})=f(\frac{1}{5})=\frac{125}{(\frac{1}{5})^3}=125*125\).

\({f(5x)}*{f(\frac{x}{5})}={f(5)}*{f(\frac{1}{5})}=125^2\) and since \(f(x) = f(1)=125\), then \({f(5x)}*{f(\frac{x}{5})}=125^2=(f(x))^2\).

Answer: A.

Hope it's clear.
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Can we take constant 5 outside of f(5x) i.e 5f(x) ?
I was able to arrive at the answer by taking constant outside of the function,but not sure whether it is correct approach or not.
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 25 Aug 2013, 06:41
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manulath
If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(\frac{f(5x)}{f(x/5)}\) in terms of f(x)?

A. \((f(x))^{2}\)

B. \(f(x^{2})\)

C. \((f(x))^{3}\)

D. \(f(x^{3})\)

E. \(f(125x)\)

In order the answer to be A, the question should read:

If \(f(x) = \frac{125}{x^{3}}\), what is the value of \(f(5x)*f(x/5)\) in terms of f(x)?

Say \(x=1\), then:

\(f(x) = f(1)=\frac{125}{1^{3}}=125\);

\(f(5x)=f(5)=\frac{125}{5^3}=1\);

\(f(\frac{x}{5})=f(\frac{1}{5})=\frac{125}{(\frac{1}{5})^3}=125*125\).

\({f(5x)}*{f(\frac{x}{5})}={f(5)}*{f(\frac{1}{5})}=125^2\) and since \(f(x) = f(1)=125\), then \({f(5x)}*{f(\frac{x}{5})}=125^2=(f(x))^2\).

Answer: A.

Hope it's clear.

Can we take constant 5 outside of f(5x) i.e 5f(x) ?
I was able to arrive at the answer by taking constant outside of the function,but not sure whether it is correct approach or not.
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It depends on HOW are you doing that. Please show your work.
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 25 Aug 2013, 11:21
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f(5x) = 5f(x)
f(x/5)= 1/5f(x)
Then;
f(5x)*f(x/5) = 5f(x)*1/5f(x) =
\((f(x))^2\)

Is this approach fine?
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 25 Aug 2013, 11:36
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f(5x) = 5f(x)
f(x/5)= 1/5f(x)
Then;
f(5x)*f(x/5) = 5f(x)*1/5f(x) =
\((f(x))^2\)

Is this approach fine?
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No, that's not correct.

\(f(x) = \frac{125}{x^{3}}\),
\(f(5x) = \frac{125}{(5x)^{3}}=\frac{1}{x^3}\).
\(f(\frac{x}{5}) = \frac{125}{(\frac{x}{5})^{3}}=\frac{125^2}{x^3}\).

So, \(f(x)=125*f(5x)\) and \(f(\frac{x}{5})=125*f(x)\)

Hope it helps.
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 02 Sep 2014, 03:31
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\(f(5x) * f(\frac{x}{5}) = \frac{125}{(5x)^3} * \frac{125}{(\frac{x}{5})^3}= \frac{125}{x^3} * \frac{125}{x^3} = [f(x)]^2\)

Answer = A
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 18 Jul 2017, 19:29
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This can be solved like this. It is important to understand the difference between (a) and (b) for instance (F(x))^2 means you square the whole function while F(x^2) means you plug in X^2 everytime you see X. A good video explaining how function notation works is here. It's not my video but he explains it well if you missed this step.

https://www.youtube.com/watch?v=T6-Zdr5w_bE
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms 12 Nov 2024, 03:05
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