Q. 225.0( 1 Vote )

# Mark the correct alternative in each of the following:

Let f : R –{n} → R be a function defined by where m ≠ n. Then,

A. f is one-one onto

B. f is one-one into

C. f is many one onto

D. f is many one into

Answer :

Given that f : R –{n} → R where

Let f(x) = f(y)

⇒ (x-m)(y-n)=(x-n)(y-m)

⇒ xy – xn – my + mn = xy – xm – ny + mn

⇒ x = y

So, f is one-one.

⇒ y(x-n)=(x-m)

⇒ xy – ny = x – m

⇒ x(y-1) = ny – m

For y = 1 , no x is defined.

So, f is into.

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