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* represents a certain function for all real numbers. If (1*)*=6

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* represents a certain function for all real numbers. If (1*)*=6  [#permalink]

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New post Updated on: 08 Sep 2018, 11:30
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* represents a certain function for all real numbers. If (1*)* = 6, which of the following could be true for all values of m?

(A) m*= 2m\(^3\)
(B) m* = m(m+1)
(C) m* = (2m)\(^3\)
(D) m* = 3m\(^2\)
(E) m* = m(m-1)(m+1)

Does anyone knows how to solve this question? I have tried to solved and unserstand it but it is not making any sence to me! I know the answer but even like that I just don´t understand it.Thank you for your help!

Originally posted by FilipaFontao on 08 Sep 2018, 01:47.
Last edited by generis on 08 Sep 2018, 11:30, edited 2 times in total.
Edited and formatted the question, renamed the topic
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Re: * represents a certain function for all real numbers. If (1*)*=6  [#permalink]

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New post 08 Sep 2018, 04:07
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FilipaFontao wrote:
"*" represents a certain function for all real numbers. If (1*)* = 6, which of the following could be true for all values of m?

(A) m*= 2m^3
(B) m* = m(m+1)
(C) m* = (2m)^3
(D) m* = 3m^2
(E) m* = m(m-1)(m+1)

Does anyone knows how to solve this question? I have tried to solved and unserstand it but it is not making any sence to me! I know the answer but even like that I just don´t understand it.

Thank you for your help!


Here the '*' represents a function.
Given, (1*)* = 6 implies that the function under discussion has been applied twice on the real number 1 and the result is 6.

Since it is a COULD BE TRUE type question, we have to analyze each of the options till we arrive at the correct answer.

A. m*= \(2m^3\)
Our only reference in hand is (1*)* = 6.-----------(a)
Let's put m=1, then 1*=2(1^3)=2---------------(b)
Let's apply '*' function again, we have (1*)*=2* (Since 1*=2 from (b))
Now, 2*=\(2(2^3)=8\neq{6}\) (DISCARD)

B. m* = m(m+1)
Put m=1, we have
1*=1(1+1)=2
Let's apply '*' function again, we have (1*)*=2* (Since 1*=2 from (b))
Now, 2*=2(2+1)=6.
So, (1*)*=2*=6 (MATCHED)

Ans. (B)

P.S:- We have tried m=1 since we have given (1*)*=6.
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Re: * represents a certain function for all real numbers. If (1*)*=6   [#permalink] 08 Sep 2018, 04:07
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* represents a certain function for all real numbers. If (1*)*=6

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