Question

If $f: X \rightarrow Y$ is an onto function, if and only if the range of $f$ will be:

• A. $X$
• B. $X \cap Y$
• C. $Y$
• D. $X \cup Y$

Hint:

In an onto function, the range is equal to the entire codomain.

Answer 1

The Correct Option is C

Step 1: Definition of onto function.
An onto function (also called surjection) is a function in which every element of the codomain (set $Y$) has a pre-image in the domain (set $X$). This means that for every $y \in Y$, there exists an $x \in X$ such that $f(x) = y$.

Step 2: Range of an onto function.
Since an onto function maps every element of $Y$ to at least one element in $X$, the range of $f$ will cover the entire set $Y$. Hence, the range of $f$ is $Y$.

Step 3: Conclusion.
Therefore, the correct answer is (C) $Y$.