Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x) = x – 2/ x – 3 ∀ x ∈ A . Then show that f is bijective.

Let A = R - \{ 3 \} , B = R - \{ 1 \}  . Let f : A \rightarrow B  be defined by f(x) = x - 2/ x - 3 \forall x \in A . Then show that f is bijective.

Answers (1)

Here,

A = R - \{ 3 \} , B = R - \{ 1 \} \\

f : A \rightarrow B  be defined by f (x) = x - 2/ x - 3 \forall x \in A\\

Hence, f (x) = (x - 3 + 1)/ (x - 3) = 1 + 1/ (x - 3)\\

Say  f(x1) = f (x2)\\

1+\frac{1}{x_{1}-3}=1+\frac{1}{x_{2}-3}

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

So, f (x) is an injective function.

\\If, y = (x - 2)/ (x -3)\\ Or, x - 2 = xy - 3y\\ Or, x(1 - y) = 2 - 3y\\ Or, x = (3y - 2)/ (y - 1)\\ Or, y \in R - \{ 1 \} = B\\

So, f (x) is onto or subjective.

Therefore, f(x) is a bijective function.

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question