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Let f(x) = 1/ax+b where a and b are nonzero constants. Find all solutions to f^{-1}(x) = 0. Express your answer in terms of a and/or b.

 Feb 8, 2018
 #1
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There are a lot of ways to think about this, but here's one way.

 

Also I'm assuming that   f(x)  =  1 / (ax + b) .

 

f-1( x )  =  0         We want to solve for  x . Apply the function  f  to both sides of the equation.

 

f( f-1( x ) )   =   f( 0 )

 

x   =   f(0)

 

x   =   1 / (a(0) + b)

 

x  =   1 / b          For  f  to be a function,  1/b  must be the only value of  f(0) .

 

So...

 

f-1( 1/b )   =   0

 

The only solution to  f-1(x)  =  0    is   x  =  1/b .

 Feb 8, 2018

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