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Given that $f(3)=5$ and $f(3x)=f(x)+2$ for all $x$, find $f^{-1}(11)$.

Creeperhissboom  May 22, 2018
 #1
avatar+92674 
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If  f(3)  = 5   and    f(3x)  = f(x) + 2, then .....

 

f(3x)  = f(3) + 2     implies that x  = 3

 

So

 

f(3 * 3)  = f(3) + 2

f(9)  =  5 + 2

f(9)  = 7

 

And

f(3x)  = f(9) + 2   implies that  x  = 9...so.....

f(3*9) = f(9) + 2

f(27)  = 9

 

And

 

f(3x)  = f(27) + 2   implies that x  = 27

f(3 * 27)  = f(27) + 2

f(81)  = 9 + 2

f(81) = 11

 

And   (81, 11)  is on the original graph  .....so  (11, 81)  is on the inverse

 

So

 

f-1(11)  =  81

 

 

cool cool cool

CPhill  May 22, 2018

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