Let `f:AtoB`. Find f(A), i.e, the range of f, if f is an onto function.

Answer

To find the range of the function \( f: A \to B \) given that \( f \) is an onto function, we can follow these steps:

### Step 1: Understand the definition of an onto function
An onto function (or surjective function) is defined such that every element in the codomain \( B \) has at least one pre-image in the domain \( A \). This means that for every \( b \in B \), there exists at least one \( a \in A \) such that \( f(a) = b \).

### Step 2: Identify the implications of being onto
Since \( f \) is onto, it implies that all elements of the set \( B \) are covered by the function \( f \). Therefore, there are no elements in \( B \) that are left out when we apply the function \( f \) to the elements of \( A \).

### Step 3: Determine the range of \( f \)
The range of a function \( f \), denoted as \( f(A) \), is the set of all images of elements in \( A \) under the function \( f \). Given that \( f \) is onto, the range of \( f \) will be equal to the entire set \( B \). This is because every element of \( B \) has a corresponding element in \( A \) that maps to it.

### Conclusion
Thus, if \( f \) is an onto function, the range \( f(A) \) is equal to \( B \):
\[ f(A) = B \]