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Let f(x)=1/(ax+b) where a and b are nonzero constants. Find all solutions to f^(-1)(x) = 1. Express your answer in terms of a and/or b.

 Jul 6, 2022
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y = 1  / ( ax + b)     get x by itself

 

y ( ax + b)  = 1

 

ay x  + by  = 1

 

ay x      = 1 - by

 

x = ( 1 - by) /( ay)         swap x and y

 

y = (1 - bx) / (ax)  =  f-1 (x)

 

1 =  (1 - bx) / (ax)

 

ax = 1 - bx

 

ax - bx = 1

 

x ( a - b) = 1

 

x = 1  / ( a  -  b )

 

 

cool cool cool

 Jul 6, 2022

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