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If \(f(3)=1\) and \(f(2x)=2f(x)\) for all \(x\) , find \(f^{-1}(64)\).

tertre  Mar 10, 2018
 #1
avatar+91141 
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f(3)  =  1

f(6)  = f(2 * 3) = 2f(3)  = 2 * 1  = 2

f(12)  = f(2 * 6)  = 2f(6)  = 2 * 2  = 4

f(24)  = f(2 * 12) = 2f(12) = 2 * 4 = 8

f(48) = f(2 * 24)= 2f(24) = 2 * 8   = 16

f(96) = f(2 *48) = 2f(48) = 2 * 16 = 32

f(192) = f(2 * 96) = 2f(96) = 2 * 32  = 64

 

So

 

f(192)  =  64       which implies that

 

f-1(64)  =  192

 

 

cool cool cool

CPhill  Mar 10, 2018

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