Test Index

BITSAT 2014 Paper

Section: Mathematics

© examsnet.com

Question : 104 of 150

Marks: +1, -0

Let f : R → R be a function defined by f (x) =

\frac{x-m}{x-n}

, where m ≠ n , then

f is one-one onto
f is one-one into
f is many-one onto
f is many-one into

Solution:

Let f : R → R be a function defined by

f (x) =

\frac{x-m}{x-n}

For any (x, y) ∊ R

Let f (x) = f (y)

⇒

\frac{x-m}{x-n}

=

\frac{y-m}{y-n}

⇒ x = y

∴ f is one – one

Let α ∊ R such that f (x) = α

⇒ α =

\frac{x-m}{x-n}

⇒ (x - n) α = x - m

⇒ x α - n α = x - m

⇒ x α - x = nα - m

⇒ x (α - 1) = nα - m

⇒ x =

\frac{n\alpha - m}{\alpha - 1}

, for α = 1 , x ∉ R

So, f is not onto

© examsnet.com

Go to Question:

Prev Question

Next Question