Question

Let \( A = \{1,2,3\} \) and \( B = \{2,4,6\} \). A function \( f : A \to B \) is defined by \( f(x)=2x \). The function is:

• A. One-one only
• B. Onto only
• C. Both one-one and onto
• D. Neither one-one nor onto

Hint:

To verify one-one: Check if \( f(x_1) = f(x_2) \) implies \( x_1 = x_2 \).
To verify onto: Check if the range of the function equals its codomain. If \( |A| = |B| \) and the function is one-one, it must also be onto.

Answer 1

The Correct Option is C