Back at it again with the real line

Algebra Level 3

If f ( x ) = x 2 + 14 x + 42 f(x)=x^2+14x+42 find the number of real solutions of f ( f ( f ( f ( . . . ( f ( x ) ) . . . ) ) ) ) f(f(f(f(...(f(x))...)))) without multiplicity. Clarification: 25 ! 25! times compound, where ! ! denotes the factorial function


The answer is 2.

Ραμών Αδάλια by Ραμών Αδάλια , 22, Spain

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1 solution

f ( x ) = ( x + 7 ) 2 − 7 f(x)=(x+7)^2-7

f ( f ( x ) ) = ( x + 7 ) 4 − 7 f(f(x))=(x+7)^4-7

f ( f ( f ( x ) ) ) = ( x + 7 ) 8 − 7 f(f(f(x)))=(x+7)^8-7

It is easy to see a pattern and that it will always have two real solutions without multiplicity

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Of course, induction will help to prove the pattern ;)

Ραμών Αδάλια - 5 years, 3 months ago

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