) if f(x) = ax + b,
f(f(f(x)))=8x + 21
Find the value of a + b =?
a)2 b)6 c)5 d)7

• f(f(f(x)))=8x+21
  f(f(ax+b))=8x+21
  f(a(ax+b)+b)=8x+21
  a(a(ax+b)+b)+b=8x+21
  a^3(x)+aab+ab+b=8x+21
  Comparing similar terms we get:
  a^3(x)=8x
  Therefore, a=2;
  putting the value of a in aab+ab+b=21
  4b+b+b=21
  7b=21
  b=3
  a+b=2+3=5
• 5 years agoHelpfull: Yes(11) No(0)
• c) 5
  the equation will be
  a(a(ax+b)+b)+b=8x+ 21
  we get by solving it
  a=2;
  b=3;
  so a+b=5;
• 5 years agoHelpfull: Yes(8) No(0)
• f(x)=ax+b ------------------------(1)
  f(f(f(x)))=8x+21----------------------(2)
  Putting (1) in (2) we get,
  a3x+a2b+ab+b=8x+21
  Taking x=0
  We get,
  a2b+ab+b-21=0 ie.a2b+ac+d=0
  Solve a :using -b+b2-4ac/2a
  We get at final step, -b+-3b2+84b /2b
  Take b=1;
  We will get a=4
  Hence b=1(substitute back to any equation)
  SO a+b=5;
  
  ans:C-5
• 5 years agoHelpfull: Yes(1) No(0)
• 5 ia the correct answer
• 5 years agoHelpfull: Yes(1) No(0)
• c) 5
  the equation will be
  a(a(ax+b)+b)+b=8x+ 21
  on comparing both side we can get
  a=2;
  b=3;
  so a+b=5;
• 5 years agoHelpfull: Yes(1) No(0)
• ans:-2
  by option vertification
  ax^3+a^2b+ab+b=8x+b
• 5 years agoHelpfull: Yes(0) No(0)
• f(f(ax+b))=8x+21
  f(a(ax+b)+b)=8x+21
  a(a(ax+b)+b)+b=8x+21
  a(a^2x+ab+b)
  a^3x+a^2b+ab+b=8x+21
  there fore a^3x=8x
  a=2:
  8x+4b+2b+b=8x+7b
  there fore 7b=21;
  b=3
  a=2:b=3:a+b=5:
• 4 years agoHelpfull: Yes(0) No(0)