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Let \[f(x) = \frac{2x + 3}{kx - 2}.\]Find all real numbers $k$ so that $f^{-1}(x) = f(x).$

 

 

I answered (-inf, inf) but its wrong.

 

interval notation

 
 Jan 8, 2022
 #1
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I'll start by stating that I do not have a clue.

 

Now the discussion:

 

when x=0     k can be anything

But, for any other given x,  k cannot equal 2/x     

 

But I don't know what the answer is.     I tried graphing it but that just confused me more.  frown

 

Maybe it is    \((-\infty, \frac{2}{x}) \cup (\frac{2}{x},\infty)\)    where   \(x\ne 0\)           But I am guessing.  

 
 Jan 9, 2022

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