Latest TCS Aptitude Question SOLUTION: ) 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

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) 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

Asked In TCS prabhu (5 years ago)

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Stanzin Kadol  (5 years ago)

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

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ankur kumar garg  (5 years ago)

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;

Is this solution Helpfull? Yes (8) | No   

  (5 years ago)

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

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Prikshit Gakhar  (5 years ago)

5 ia the correct answer

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rishabh kumar  (5 years ago)

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;

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prasanna  (5 years ago)

ans:-2
by option vertification
ax^3+a^2b+ab+b=8x+b

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penti Saipriya  (4 years ago)

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:

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