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

Question

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)

Bunuel · Accepted Answer

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.

SVaidyaraman · Answer

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}

manulath · Answer

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.

Bunuel · Answer

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blueseas · Answer

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

mneeti · Answer

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!

Bunuel · Answer

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)).

mneeti · Answer

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!

Bunuel · Answer

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)?

abid1986 · Answer

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.

Bunuel · Answer

It depends on HOW are you doing that. Please show your work.

abid1986 · Answer

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?

Bunuel · Answer

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.

PareshGmat · Answer

f(5x) * f(\frac{x}{5}) = \frac{125}{(5x)^3} * \frac{125}{(\frac{x}{5})^3}= \frac{125}{x^3} * \frac{125}{x^3} =  ^2

Answer = A

SamBoyle · Answer

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

Attachments

Function question 11.png [ 324.86 KiB | Viewed 21728 times ]

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

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

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