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Suppose that \( f(x) = \frac{1} { 2x + b}. \) For what value of b does \( f ^-1(x) = \frac{1-2x} { 2x}?\)

 Feb 21, 2018
 #1
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f(x)  =   1 / [2x + b]

 

Let's find the  inverse

 

For  f(x)  write  y

 

y  =  1 /[ 2x + b ]        multiply both sides by  2x + b

 

y ( 2x + b)  =  1

 

2xy + yb  =  1

 

2xy  =  1 - yb

 

x  =   [ 1 - yb]  / [2y]         "swap"  x  and y

 

y  =  [ 1 - bx] / [ 2x]      for y, write  f-1(x)

 

f-1(x)  =  [ 1 - bx ] / [ 2x ]

 

So....it's obvious that b  = 2

 

 

cool cool cool

 Feb 21, 2018

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