Let A = R – {3} and B = R– {2/3}. If f: A → B : f(x) = (2x-4)/(3x-9) , then prove that f is a bijective function.

Question

Let A = R – {3} and B = R– {\(\frac{2}{3}\)}. If f: A → B : f(x) =  \(\frac{2x-4}{3x-9}\) , then prove that f is a bijective function.

Answer 1

One - One : Let x₁,x₂ be any two elements of A, then

Hence, f is one-one function  ...(i)

Onto : 

Hence, f is onto function   ...(ii)

(i) and (ii) 

⇒ f is one-one onto i.e. bijective function.