Latest CTS Aptitude Question SOLUTION: if f(f(X))=81. then. value of x=? when f(X)=2X-1+f(X-1). is not equal to zero and f(X=0)=0

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if f(f(X))=81. then. value of x=?
when f(X)=2X-1+f(X-1). is not equal to zero and f(X=0)=0

Asked In CTS vamshi krishna (10 years ago)

Solved Ann Theressa Read Solution (6)

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Read Solution (6) :

Ann Theressa  (10 years ago)

f(X=0) = 0

f(X=1) = 2*1-1+f(1-1)
= 2-1+0
= 1

f(X=2) = 2*2-1+f(2-1)
= 4-1+1
= 4

f(X=3) = 2*3-1+f(3-1)
= 6-1+4
= 9

===>f(X=n) = n^2
f(f(X)) = 81
X = sqrt(sqrt(81)) = 3

Is this solution Helpfull? Yes (32) | No   

Mani kandan  (10 years ago)

f(X=0) = 0

f(X=1) = 2*1-1+f(1-1)
= 2-1+0
= 1

f(X=2) = 2*2-1+f(2-1)
= 4-1+1
= 4

f(X=3) = 2*3-1+f(3-1)
= 6-1+4
= 9

===>f(X=n) = n^2
f(f(X)) = f(f(x=3)) = f(x=9)=9^2=81 [ i.e, f(x=3)=3^2=9]

so ans is x=3.

Is this solution Helpfull? Yes (6) | No   

Dimple  (10 years ago)

f(f(X))=81
X=3

Is this solution Helpfull? Yes (2) | No (3)  

Shikha Sinha  (9 years ago)

x=9, we find f(1)=1,f(2)=4,f(3)=9,f(4)=16... so f(9)=81.

Is this solution Helpfull? Yes (2) | No (2)  

Shivakar Kumar  (6 years ago)

f(f(x))=81

f(x)*f(x)=81
9*9=81 //only possible value for f(x)=9

it's means f(x)=9 not for x=9
so, let we go to find what of x=f(x)=9

in problem f(x)=2x-1+f(x-1) and f(x=0)=0

so put x=1 in f(x)
we find
f(X=1) = 2*1-1+f(1-1) means
f(1)=2*1-1+f(1-1)
= 2-1+f(0) //f(0)=0 according to question
=2-1+0
= 1

and now put 2 in f(x)
f(X=2) = 2*2-1+f(2-1)
= 4-1+f(1) //we already find f(1) that is 1 so we simply put f(1) value
= 4-1+1
=4

now we put x=3 in f(x)
f(X=3) = 2*3-1+f(3-1)
f(3)=2*3-1+f(3-1)
= 6-1+f(2) //we already find f(2)=4 not f(3-1)=2
= 6-1+4
=9

so, x=3 that is put in f(x) that gives f(3)=9

f(x)*f(x)=81
f(3)*f(3)=81
9*9=81

X=3 Ans

Is this solution Helpfull? Yes (1) | No   

souharda  (9 years ago)

function=81 x=3

Is this solution Helpfull? Yes | No   

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