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If f(x) = (x-3)/(x-4), then for what value of x is f^-1(x) undefined?

 Jan 25, 2018
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f(x)  =  (x - 3)/(x - 4)

                                     First let's find  f-1(x) . Instead of  f(x) , write  y .

y   =   (x - 3)/(x - 4)

                                     Now solve for  x . Multiply both sides of the equation by  (x - 4) .

y(x - 4)   =   x - 3

 

xy - 4y   =   x - 3

                                    Add  4y  to both sides and subtract  x  from both sides.

xy - x   =   4y - 3

                                    Factor  x  out of the terms on the left side.

x(y - 1)   =   4y - 3

                                    Divide both sides by  (y - 1) .

x   =   (4y - 3)/(y - 1)

                                    So...

f-1(x)  =  (4x - 3)/(x - 1)

 

And...

 

(4x - 3)/(x - 1)  is undefined when  x - 1  =  0

 

f-1(x)  is undefined when  x = 1

 Jan 25, 2018

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