Let `A=R-{3}a n dB=R-{1}dot` Consider the function `f: Avec` defined by `f(x)=(x-2)/(x-3)dot` Show that is one-one and onto and hence find `f^(-1)`

Explanation

`A=R-{3}`


`B=R-{1}`


`f: A -> B`


`f(x)=frac{x-2}{x-3}`


`f(x_{1})=f(x_{2})`


`frac{x_{1}-2}{x_{1}-3}=frac{x_{2}-2}{x_{2}-3}`


`(x_{2}-3)(x_{1}-2)=(x_{2}-2)(x_{1}-3)`


`x_{1} x_{2}-3 x_{1}-2 x_{2}+6=x_{1} x_{2}-3 x_{2}-2 x_{1}+6`


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