Menu Close

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




Question Number 1280 by Rasheed Soomro last updated on 19/Jul/15
 f ( (1/(f(x))))=f(x)   f(x)=?
f(1f(x))=f(x)f(x)=?
Commented by 123456 last updated on 19/Jul/15
f(x)=(1/x)
f(x)=1x
Commented by prakash jain last updated on 19/Jul/15
f(x)=((ax+b)/(cx+d))  f((1/(f(x))))=((a((cx+d)/(ax+b))+b)/(c((cx+d)/(ax+b))+d))=((ax+b)/(cx+d))  [a(b+c)x+(b^2 +ad)](cx+d)]=[(c^2 +ad)x+d(b+c)](ax+b)  ac(b+c)=a(c^2 +ad)⇒bc=ad  b^2 c+acd+abd+acd=ad(b+c)+(c^2 +ad)b      ⇒b^2 c+acd=c^2 b+abd⇒bc=ad  d(b^2 +ad)=bd(b+c)      ⇒db^2 +ad^2 =b^2 d+bcd⇒bc=ad  f(x) = ((ax+b)/(cx+((bc)/a))) = ((a^2 x+ab)/(acx+bc))  This functional equation will also  have multiple solutions.
f(x)=ax+bcx+df(1f(x))=acx+dax+b+bccx+dax+b+d=ax+bcx+d[a(b+c)x+(b2+ad)](cx+d)]=[(c2+ad)x+d(b+c)](ax+b)ac(b+c)=a(c2+ad)bc=adb2c+acd+abd+acd=ad(b+c)+(c2+ad)bb2c+acd=c2b+abdbc=add(b2+ad)=bd(b+c)db2+ad2=b2d+bcdbc=adf(x)=ax+bcx+bca=a2x+abacx+bcThisfunctionalequationwillalsohavemultiplesolutions.

Leave a Reply

Your email address will not be published.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