BITSAT 2014 Paper

Let f : R → R be a function defined by

f (x) =

x−m

x−n

For any (x, y) ∊ R
Let f (x) = f (y)
⇒

x−m

x−n

=

y−m

y−n

⇒ x = y
∴ f is one – one
Let α ∊ R such that f (x) = α
⇒ α =

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 = nα−mα−1 , for α = 1 , x ∉ R
So, f is not onto