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Given that \(f(2)=5\) and \(f^{-1}(x+4)=2f^{-1}(x)+1\) for all \(x\) , find \(f^{-1}(17)\).

 Feb 28, 2018
 #1
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If  f (2)  = 5

 

Then   this implies that :

 

f-1 (5)  = 2   ...so....

 

2f-1 (5) + 1   =   f-1 (5 + 4)

2*2 + 1 =  f-1 ( 5 + 4)

5 = f-1 (9)  

 

2f-1(9) + 1 =  f-1(9 + 4)

2*5 + 1  = f-1(13)

11 =  f-1 (13)

 

2 f-1 (13) + 1    =  f-1(13 + 4)

2  * 11 + 1  =  f-1 (17)

23 = f-1(17)

 

 

cool cool cool

 Feb 28, 2018
edited by CPhill  Feb 28, 2018

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