Onto Function or Surjective - Practice Questions & MCQ

A function $f: X \rightarrow Y$ is said to be onto (or surjective), if every element of $Y$ is the image of some element of $X$ under $f$, i.e., for every $y \in Y$, there exists an element $x$ in $X$ such that $f(x)=y$

Hence, Range = co-domain for an onto function

Some examples of onto function
Consider, $X=\left\{x_1, x_2, x_3, x_4\right\}$ and $Y=\left\{y_1, y_2, y_3\right\} \mid$

$
f: X \rightarrow Y
$
 

As every element in Y has a pre-image in X, so it is an onto function

Method to show onto or surjective

Find the range of $y=f(x)$ and show that range of $f(x)=$ co-domain of $f(x)$

Number of onto functions