Menu Close

f-x-2-f-x-1-




Question Number 1180 by 934111 last updated on 11/Jul/15
f(x^2 )−f(x)=1
$${f}\left({x}^{\mathrm{2}} \right)−{f}\left({x}\right)=\mathrm{1} \\ $$
Commented by 123456 last updated on 11/Jul/15
{0,1}∉D(f)
$$\left\{\mathrm{0},\mathrm{1}\right\}\notin\mathrm{D}\left({f}\right) \\ $$
Answered by prakash jain last updated on 13/Jul/15
f(x)=log_2 log_k x  f(x^2 )=log_2 log_k x^2   =log_2 (2log_k x)=1+log_2 log_k x=1+f(x)
$${f}\left({x}\right)=\mathrm{log}_{\mathrm{2}} \mathrm{log}_{{k}} {x} \\ $$$${f}\left({x}^{\mathrm{2}} \right)=\mathrm{log}_{\mathrm{2}} \mathrm{log}_{{k}} {x}^{\mathrm{2}} \\ $$$$=\mathrm{log}_{\mathrm{2}} \left(\mathrm{2log}_{{k}} {x}\right)=\mathrm{1}+\mathrm{log}_{\mathrm{2}} \mathrm{log}_{{k}} {x}=\mathrm{1}+{f}\left({x}\right) \\ $$
Commented by Rasheed Ahmad last updated on 13/Jul/15
Appreciation for your intelligence  and knowledge. I would like to  ask you how did you determine  that? Is there any method for  solving  such eqns?
$${Appreciation}\:{for}\:{your}\:{intelligence} \\ $$$${and}\:{knowledge}.\:{I}\:{would}\:{like}\:{to} \\ $$$${ask}\:{you}\:{how}\:{did}\:{you}\:{determine} \\ $$$${that}?\:{Is}\:{there}\:{any}\:{method}\:{for} \\ $$$${solving}\:\:{such}\:{eqns}? \\ $$
Commented by prakash jain last updated on 13/Jul/15
Derived using f(xy)=f(x)+f(y)  ⇒f(x)=log x  If multiplication of a variable results in  addition f(x^2 )=f(x)+1 then function will  be logarithmic.
$$\mathrm{Derived}\:\mathrm{using}\:{f}\left({xy}\right)={f}\left({x}\right)+{f}\left({y}\right) \\ $$$$\Rightarrow{f}\left({x}\right)=\mathrm{log}\:{x} \\ $$$$\mathrm{If}\:\mathrm{multiplication}\:\mathrm{of}\:\mathrm{a}\:\mathrm{variable}\:\mathrm{results}\:\mathrm{in} \\ $$$$\mathrm{addition}\:{f}\left({x}^{\mathrm{2}} \right)={f}\left({x}\right)+\mathrm{1}\:\mathrm{then}\:\mathrm{function}\:\mathrm{will} \\ $$$$\mathrm{be}\:\mathrm{logarithmic}. \\ $$
Commented by Faaiz Soomro last updated on 13/Jul/15
Thanks Parkash Jain.I am learning from you.
$${Thanks}\:{Parkash}\:{Jain}.{I}\:{am}\:{learning}\:{from}\:{you}. \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *