If $f: X \rightarrow Y$ is an onto function, if and only if the range of $f$ will be:
Show Hint
- $X$
- $X \cap Y$
- $Y$
- $X \cup Y$
The Correct Option is C
Solution and Explanation
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) $Y$.
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