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Onto Function or Surjective - (Concept)
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
| Exam | Chapter |
| JEE MAIN | Sets, Relations and Functions |
In the case of an onto function, which of the following is true?
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The number of functions f from {1,2,3,........,20} onto {1,2,3,........,20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is:
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Let A = {x1,x2,x3......,x7} and B = { y1 ,y2 ,y3 } be two sets containing seven and three distinct elements respectively. Then the total number of functions : A
B that are onto, if there exist exactly three elements x in A such that
(x) = y2, is equal to :
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If n(A) = 5 and n(B) = 3. Find the number of onto functions A to B.
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If n(A)= 3 and n(B)= 5. Find the number of onto functions from A to B.
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If n(A) =2 and n(B) = 2. Find the number of onto functions from A to B.
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Let such that
and g be any arbitrary function. Which of the following statement is NOT true?
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Which of the graphs shows a surjective function ?
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For real x, let then
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Let Then the number of elements in the set
is___________.
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Let be the relation defined by :
. The correct statement is:
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Let R = {a, b, c, d, e} and S = {1, 2, 3, 4}. Total number of onto functions f: R S such that f(a)
1, is equal to _______.
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$f:(-\infty, \infty) \rightarrow[0, \infty), f(x)=x^2$ is a/an:
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Find the number of onto functions from $A$ to $B$ where $n(A)=5$ and $n(B)=3$.
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$\begin{aligned} & \text { If } f(x)=2 x^3-1, g(x)=\frac{x^2}{x^2+1}, \\ & \left.h(x)=\mid \log x+x^3+\sqrt[3]{x}\right]{\text {, then }}\end{aligned}$
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Let $A=\{1,2,3, \ldots, n\}$ and $B=\{a, b\}$. Then the number of surjections from A to B is
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The function $y=\frac{x+1}{2x+1}$ is
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Let $\mathbb{R}$ be the set of all real numbers and $f: \mathbb{R} \rightarrow \mathbb{R}_{\text {be a continuous function. Suppose }}|f(x)-f(y)| \geq|x-y|_{\text {for }}$ all real numbers $x$ and $y$. Then
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Let $f:[0,3] \rightarrow \mathrm{A}$ be defined by $f(x)=2 x^3-15 x^2+36 x+7$ and $g:[0, \infty) \rightarrow B$ be defined by $\mathrm{g}(\mathrm{x})=\frac{\mathrm{x}^{2025}}{\mathrm{x}^{2025}+1}$. If both the functions are onto and $\mathrm{S}=\{\mathrm{x} \in \mathbf{Z}: \mathrm{x} \in \mathrm{A}$ or $\mathrm{x} \in \mathrm{B}\}$, then $\mathrm{n}(\mathrm{S})$ is equal to:
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Definition 6 A function f : X 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 Y, there exists
