Show that a one-one function f: {1, 2, 3} rig | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(N/A) Let $A = \{1, 2, 3\}$. The function $f: A \rightarrow A$ is given as one-one.By the definition of a one-one function,distinct elements in the do

Vedclass · Accepted Answer

Vedclass · Answer

(N/A) Let $A = \{1, 2, 3\}$. The function $f: A \rightarrow A$ is given as one-one.
By the definition of a one-one function,distinct elements in the domain $A$ must map to distinct elements in the codomain $A$.
Since the domain $A$ has $3$ elements,their images $f(1), f(2),$ and $f(3)$ must be $3$ distinct elements of the codomain $A$.
Because the codomain $A$ also contains exactly $3$ elements,the set of images ${f(1), f(2), f(3)}$ must be equal to the entire codomain $A$.
Therefore,every element in the codomain has a pre-image in the domain,which satisfies the definition of an onto function.
Thus,$f$ must be onto.

Show that a one-one function $f: \{1, 2, 3\} \rightarrow \{1, 2, 3\}$ must be onto.

Similar Questions

If $f: R \rightarrow C$ is defined by $f(x)=e^{2 i x}$ for $x \in R$,then $f$ is (where $C$ denotes the set of all complex numbers)

Let $f(x) = \begin{cases} -a & \text{if } -a \leq x \leq 0 \\ x+a & \text{if } 0 < x \leq a \end{cases}$ where $a > 0$ and $g(x) = \frac{f(|x|) - |f(x)|}{2}$. Then the function $g: [-a, a] \rightarrow [-a, a]$ is

Let $f: R \to R$ be a function defined by $f(x) = \frac{x - m}{x - n}$,where $m \ne n$. Then

For real $x,$ let $f(x) = x^3 + 5x + 1,$ then

The function $f: C \rightarrow C$ defined by $f(x) = \frac{ax + b}{cx + d}$ for $x \in C$,where $ad - bc \neq 0$,reduces to a constant function if:

Vedclass Test Series

Exam Paper Generator

Online Exam Module