Question

If \( f : A \to B \) is an onto function, then

• A. \( f(A) \subset B \)
• B. \( f(A) = B \)
• C. \( f(A) \supset B \)
• D. \( f(A) \neq B \)

Hint:

For an onto (surjective) function, the image of the domain must be the entire co-domain. So, \( f(A) \) must equal \( B \).

Answer 1

The Correct Option is B

For a function \( f : A \to B \) to be onto (surjective), it must map every element in the domain \( A \) to an element in the co-domain \( B \) such that the range of \( f \) covers all of \( B \). This means that the image of \( A \), denoted by \( f(A) \), must be equal to the entire set \( B \). Thus, for \( f \) to be an onto function: \[ f(A) = B \] Therefore, the correct answer is: (B) \( f(A) = B \).