\(\text{If $f(x)=\dfrac{x-3}{x-4}$, then for what value of $x$ is $f^{-1}(x)$ undefined? }\)
+36916 For the ORIGINAL function x = 4 is undefined...
Let's find the inverse funtion f^-1 solve the original for x
y = (x-3)/(x-4)
yx -4y = x-3
-4y+3 = x - yx
(-4y+3) = x (1-y)
(-4y+3)/(1-y) = x Now 'switch' the x's and y's
(-4x+3)/(1-x) =y this is f^-1 and we can see that x cannot = 1 undefined at this value of x
