Four Fours

Algebra Level 3

If f ( 9 ) ( 2 x − 1 4 ) f^{(9)}(\frac {2x-1}{4}) = 2 x − 37 4 \frac{2x-37}{4} , find 4 [ f ( 4 ) ( 4 ) ] 4 4[f^{(4)}(4)]^4 .

Note : The notation f ( n ) ( x ) f^{(n)}(x) means that f ( x ) f(x) is iterated , or repeatedly carried out, n n times. For example, f ( 3 ) ( x ) f^{(3)}(x) means f ( f ( f ( x ) ) ) f(f(f(x))) .


The answer is 0.

Rhoy Omega by Rhoy Omega , 24, Philippines

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1 solution

f 9 ( 2 x − 1 4 ) = 2 x − 37 4 = 2 x − 1 4 − 9 f 4 ( 2 x − 1 4 ) = 2 x − 1 4 − 4 f 4 ( 4 ) = 4 − 4 = 0 f^{ 9 }\left( \frac { 2x-1 }{ 4 } \right) =\frac { 2x-37 }{ 4 } =\frac { 2x-1 }{ 4 } -9\\ f^{ 4 }\left( \frac { 2x-1 }{ 4 } \right) =\frac { 2x-1 }{ 4 } -4\\ f^{ 4 }\left( 4 \right) =4-4=0

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Good solution.

Rhoy Omega - 5 years, 4 months ago

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