Question

For a function \( f: A \to B \), the function will be onto if:

• A. \( f(A) \subset B \)
• B. \( f(A) = B \)
• C. \( f(A) \supset B \)
• D. None of these

Hint:

For a function to be onto (surjective), its image must cover the entire target set. If \( f(A) = B \), then \( f \) is onto.

Answer 1

The Correct Option is B

A function \( f: A \to B \) is said to be onto (or surjective) if for every element \( b \in B \), there exists an element \( a \in A \) such that \( f(a) = b \). This means that the image of \( A \) under the function \( f \) must cover the entire set \( B \). Hence, for \( f \) to be onto, the condition is: \[ f(A) = B \] This means the range of the function \( f \) is exactly equal to \( B \), which corresponds to option (B).