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Given that f(x) = x^{-1} + x/(1 + x^{-1}), f(f(-2))? Express your answer as a common fraction.

 Jul 23, 2022
 #1
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The answer is 7/2.

 Jul 23, 2022
 #2
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f (x)  =  1/x + x/[ 1 + 1/x ] =   1/x + x / ( [x + 1]  /x )  =  1/x + x^2 / (x + 1)

 

f(-2)  =  -1/2  + (-2)^2 / (-1)   =  -4 -1/2 = -9/2

 

f (f (-2)) =  f (-9/2)  =  1/ (-9/2)  + (-9/2)^2 / ( -9/2 + 1)  = 

 

-2/9  +  ( 81/4) /( -7/2)  =

 

-2/9  -  (81/4) (2/7)   =

 

-2/9  - 162 / 28   =

 

-2/9  - 81/14  =

 

-757 / 126

 

cool cool cool

 Jul 23, 2022

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