Question

Let \( f:\mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \dfrac{x - m}{x - n} \), where \( m \neq n \). 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

Hint:

Check range carefully to test surjectivity.

Answer 1

The Correct Option is B

Step 1: The function is a rational function and is injective.
Step 2: Value \(1\) is never attained, so it is not onto.