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

Guest Jul 19, 2019

#1**0 **

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

ElectricPavlov Jul 19, 2019