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If $f(x)=\dfrac{x-3}{x-4}$, then for what value of $x$ is $f^{-1}(x)$ undefined?

 May 3, 2021
 #1
avatar+11868 
+2

Hello ellapow!

 

\(y=\dfrac{x-3}{x-4}\\ x=\dfrac{y-3}{y-4}\\ x(y-4)=y-3\\ xy-4x=y-3\\ xy-y=4x-3\\ y= \dfrac{4x-3}{x-1}\)

\(f^{-1}(x)\ is\ undefined\ at\ x \in\{1\}. \)

 May 3, 2021
 #2
avatar+114087 
+1

thanks asinus :)

 

Here is the graphs

 

 

https://www.desmos.com/calculator/e2qpstbahz

 

If you want to discuss it, feel free to do so.

 May 3, 2021

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