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Manager  Joined: 12 May 2012
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If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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Question Stats: 72% (01:35) correct 28% (02:09) wrong based on 574 sessions

### HideShow timer Statistics 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. $$f(125x)$$

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.
Edited the question.
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Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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manulath wrote:
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. $$f(5x) * f(x/5) = 125 ^ 2/ x^6 = (f(x)) ^ {2}$$
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Math Expert V
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Posts: 56266
Re: If f(x)=125/x^3, what is the value of f(5x)/f(x/5) in terms  [#permalink]

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manulath wrote:
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. $$f(125x)$$

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 $${f(5x)}*{f(\frac{x}{5})}=125^2=(f(x))^2$$.

Hope it's clear.
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Re: If f(x)=125/x^3, what is the value of f(5x)/f(x/5) in terms  [#permalink]

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

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56266
Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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manulath wrote:
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. $$f(125x)$$

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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Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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SravnaTestPrep wrote:
manulath wrote:
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!
Math Expert V
Joined: 02 Sep 2009
Posts: 56266
Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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mneeti wrote:
SravnaTestPrep wrote:
manulath wrote:
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!

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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Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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Bunuel wrote:
mneeti wrote:

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!
Math Expert V
Joined: 02 Sep 2009
Posts: 56266
Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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mneeti wrote:
Bunuel wrote:
mneeti wrote:

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!

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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Re: If f(x)=125/x^3, what is the value of f(5x)/f(x/5) in terms  [#permalink]

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Bunuel wrote:
manulath wrote:
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. $$f(125x)$$

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 $${f(5x)}*{f(\frac{x}{5})}=125^2=(f(x))^2$$.

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56266
Re: If f(x)=125/x^3, what is the value of f(5x)/f(x/5) in terms  [#permalink]

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abid1986 wrote:
Bunuel wrote:
manulath wrote:
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. $$f(125x)$$

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 $${f(5x)}*{f(\frac{x}{5})}=125^2=(f(x))^2$$.

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.

It depends on HOW are you doing that. Please show your work.
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Re: If f(x)=125/x^3, what is the value of f(5x)/f(x/5) in terms  [#permalink]

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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?
Math Expert V
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Posts: 56266
Re: If f(x)=125/x^3, what is the value of f(5x)/f(x/5) in terms  [#permalink]

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abid1986 wrote:
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?

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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Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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1
$$f(5x) * f(\frac{x}{5}) = \frac{125}{(5x)^3} * \frac{125}{(\frac{x}{5})^3}= \frac{125}{x^3} * \frac{125}{x^3} = [f(x)]^2$$

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Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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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.

Attachments Function question 11.png [ 324.86 KiB | Viewed 5454 times ]

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Re: If f(x)=125/x^3, what is the value of f(5x)*f(x/5) in terms  [#permalink]

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