Let A = R – {3} and B = R – {1}. Then f:A → A : f(x) = (x - 2)/(x- 3) is

Question

Let A = R – {3} and B = R – {1}. Then \(f:A →A :f(x)=\frac{(x-2)}{(x-3)}\) is

A. one - one and into 

B. one - one and onto 

C. many - one and into 

D. many - one and onto

Answer 1

\(f:A →A :f(x)=\frac{(x-2)}{(x-3)}\)

In this function

x = 3 and y = 1 are the asymptotes of this curve and these are not included in the functions of the domain and range respectively 

therefore the function f(x) is one one sice there are no different values of x which has same value of y .

and the function has no value at y = 1 here range = codomain

∴ f(x) is onto