Question

In the function \( f : \mathbb{R} \rightarrow \mathbb{R} \), given by \( f(x) = 5x \):

• A. \( f \) is one-one onto
• B. \( f \) is many-one onto
• C. \( f \) is one-one but not onto
• D. \( f \) is neither one-one nor onto

Hint:

For linear functions like \( f(x) = ax + b \), if \( a \neq 0 \), the function is always one-to-one and onto.

Answer 1

The Correct Option is A

Step 1: Understand the function.
The given function is \( f(x) = 5x \). This is a linear function, and a linear function is always one-to-one (bijective) if the coefficient of \( x \) is non-zero.

Step 2: Conclusion.
Since the function is both one-to-one and onto, the correct answer is option (1).