+501 If $f(x)=\dfrac{x-3}{x-4}$, then for what value of $x$ is $f^{-1}(x)$ undefined?
+14995 Hello ellapow!
\(y=\dfrac{x-3}{x-4}\\ x=\dfrac{y-3}{y-4}\\ x(y-4)=y-3\\ xy-4x=y-3\\ xy-y=4x-3\\ y= \dfrac{4x-3}{x-1}\)
\(f^{-1}(x)\ is\ undefined\ at\ x \in\{1\}. \)
+118677 thanks asinus :)
Here is the graphs
https://www.desmos.com/calculator/e2qpstbahz
If you want to discuss it, feel free to do so.
