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# inverse function

+1
40
2
+500

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

May 3, 2021

#1
+11414
+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
+113177
+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