Question

{(a)Function \( f : \mathbb{R} \to \mathbb{R} \) is defined by \( f(x) = 5x, \forall x \in \mathbb{R} \). Select the correct answer:}

• A. \( f \) is onto
• B. \( f \) is many-one
• C. \( f \) is not onto
• D. \( f \) is not one-one

Hint:

To determine if a function is onto, check whether every element in the codomain has a preimage in the domain.

Answer 1

The Correct Option is A

Step 1: The function \( f(x) = 5x \) maps each real number to a unique value in \( \mathbb{R} \), ensuring it is a one-to-one mapping.
Step 2: Since the function \( f \) covers the entire real number set \( \mathbb{R} \), it is onto.
Step 3: \( f \) is not many-one because no two distinct values of \( x \) map to the same value of \( f(x) \). Hence, \( f(x) = 5x \) is onto and one-one.