F(x)=ax+b where a and b are real numbers if f(f(f(x)))=8x+21 what is the value of a+b? a)2 b)4 c)5 d)3

• f(x)=ax+b;
  f[f(x)]=a^x+ab+b
  f{f[f(f)]}=xa^3+a^2b+ab+b=8x+21
  xa^3=8x ==>a=2
  ba^2+ab+a=21 ,, put value of a=2
  then b=3
  ANS:=
  a+b=5
  
• 9 years agoHelpfull: Yes(23) No(1)
• f(f(f(x))) = a(a(ax+b)+b)+b
  = a^3.x + a^2.b + a.b + b
  =8x + 21
  Hence:
  a = 2, b = 21/(2^2 + 2 + 1)
• 9 years agoHelpfull: Yes(1) No(2)
• -1
  after solving the eq.wil be
  a3x2+2abx+(ab+b+b2)
  equating each term with 0
  then a+b=-1
• 9 years agoHelpfull: Yes(0) No(7)
• f(x)= ax + b
  f( f(x) ) = x* a^2 + ab + b
  f( f( f(x) ) ) = x* a^3 + b* a^2 + ab + b
  comparing the last equation with 8x + 21, we get :-
  a=2 and b=3. So, a+b=5
• 8 years agoHelpfull: Yes(0) No(0)