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Onto Function or Surjective - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Onto Function or Surjective is considered one the most difficult concept.
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13 Questions around this concept.
Solve by difficulty
$f:(-\infty, \infty) \rightarrow[0, \infty), f(x)=x^2$ is a/an:
Find the number of onto functions from $A$ to $B$ where $n(A)=5$ and $n(B)=3$.
Concepts Covered - 1
Onto Function or Surjective
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
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