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

Jul 19, 2019

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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

Jul 19, 2019