if f(x)=ax+b;
and f(f(f(x)))=8x+21;
then a+b=?

• f(x)= ax+b
  f(f(x))=a(ax+b)+b
  f(f(f(x)))=a[a(ax+b)+b]+b = a^3x + a^2b + ab + b = 8x + 21
  on comparing
  a^3x = 8x and a^2b + ab +b =21
  we get a=2
  then substituting value of a in a^2 + ab +b = 21
  we get 7b = 21
  b = 3
  so, a+b=5
  
  
• 10 years agoHelpfull: Yes(20) No(0)
• f(f(f(x)))=f(f(ax+b))
  =f(ax^2+ab+b)=(a^3x+a^2b+ab+b)=8x+21
  so, a^3x=8x therefore a=2
  and 4b+2b+b=21 so b=3
  2+3=5
• 10 years agoHelpfull: Yes(1) No(0)
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• 6 years agoHelpfull: Yes(1) No(1)
• f(f(f(x)))=f(f(ax+b))
  =f(ax^2+ab+b)=(a^3x+a^2b+ab+b)=8x+21
  so, a^3x=8x therefore a=2
  and 4b+2b+b=21 so b=3
  2+3=5
• 6 years agoHelpfull: Yes(0) No(0)