f ( − 55 9 ) f\left(-\frac{55}{9}\right)

Algebra Level 2

For all real numbers x x , function f f satisfies f ( x − 1 ) = f ( x + 1 ) , f ( − x ) = − f ( x ) , f ( 1 9 ) = − 16. f(x-1)=f(x+1), f(-x)=-f(x), f\left(\frac{1}{9}\right)=-16. What is the value of f ( − 55 9 ) ? f\left(-\frac{55}{9}\right)?

15 14 17 16

Ajay Dutta by Ajay Dutta , 24, India

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2 solutions

Aryaman Dubey
Mar 1, 2014

f ( − 64 9 ) f(-\frac{64}{9}) = f ( − 46 9 ) f(-\frac{46}{9})

f ( − 55 9 ) f(-\frac{55}{9}) = f ( − 37 9 ) f(-\frac{37}{9})

f ( − 46 9 ) f(-\frac{46}{9}) = f ( − 28 9 ) f(-\frac{28}{9})

f ( − 37 9 ) f(-\frac{37}{9}) = f ( − 19 9 ) f(-\frac{19}{9})

f ( − 28 9 ) f(-\frac{28}{9}) = f ( − 10 9 ) f(-\frac{10}{9})

f ( − 19 9 ) f(-\frac{19}{9}) = f ( − 1 9 ) f(-\frac{1}{9})

H e n c e , f ( − 55 9 ) Hence, f(-\frac{55}{9}) = f ( − 1 9 ) f(-\frac{1}{9})

f ( − 1 9 ) f(-\frac{1}{9}) = − f ( 1 9 ) = − ( − 16 ) = 16 -f(\frac{1}{9}) = -(-16) = \boxed{16}

H e n c e , f ( − 55 9 ) = 16 Hence, f(-\frac{55}{9})\ = \boxed{16}

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Madhuri Dholakiya
Feb 27, 2014

f(-55/9)=-f(55/9) =-f(1+46/9) =-f(46/9-1) =-f(37/9) =-f(1+28/9) =-f(28/9-1) =-f(19/9) =-f(1+10/9) =-f(10/9-1) =-f(1/9)=-(-16)=16

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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