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If f(a) = {1}/{1-a}, find the product f^{-1}(a) * a * f(a)$. (Assume a does not equal 0 and $a does not equal 1.)

WhichWitchIsWhich  Nov 2, 2017
 #1
avatar+86859 
+2

f(a) = 1 / [ 1 - a ]

 

For f(a)  write y

 

y = 1 / [ 1 - a]   rearrange as

 

[1 - a] =  1 / y

 

1 - 1/y   =  a     swap   a   and   y

 

1 - 1 / a  =  y   =  f-1 (a)  =   [ a - 1 ] / a

 

So

 

f-1 (a)   *  a  *  f(a)     =

 

 [ a - 1 ] / a    *  a    *  1 / [ 1 - a]  =

 

[a - 1]  / [ 1 - a  ]  =

 

- [ 1 - a ] / [ 1 - a ]  =      -1

 

 

 

 

cool cool cool

CPhill  Nov 2, 2017

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