Let A = {0, 1, 2, 3, 4, 5, 6, 7}. Then the nu | vedclass

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

Question

(C) Given the condition $f(1) + f(2) = 3 - f(3)$,we can rewrite it as $f(1) + f(2) + f(3) = 3$.Since $f$ is a bijective function from $A$ to $A$,all v

Vedclass · Accepted Answer

$720$

Vedclass · Answer

(C) Given the condition $f(1) + f(2) = 3 - f(3)$,we can rewrite it as $f(1) + f(2) + f(3) = 3$.Since $f$ is a bijective function from $A$ to $A$,all values $f(1), f(2), f(3)$ must be distinct elements from the set $A = \{0, 1, 2, 3, 4, 5, 6, 7\}$.The only distinct non-negative integers that sum to $3$ are $0, 1,$ and $2$.Thus,the set of values $\{f(1), f(2), f(3)\}$ must be equal to the set $\{0, 1, 2\}$.The number of ways to assign these $3$ values to $f(1), f(2),$ and $f(3)$ is $3! = 6$.The remaining $5$ elements of the domain $\{0, 4, 5, 6, 7\}$ must be mapped to the remaining $5$ elements of the codomain $\{3, 4, 5, 6, 7\}$.The number of ways to map these is $5! = 120$.Therefore,the total number of bijective functions is $3! 	imes 5! = 6 	imes 120 = 720$.

Let $A = \{0, 1, 2, 3, 4, 5, 6, 7\}$. Then the number of bijective functions $f: A \rightarrow A$ such that $f(1) + f(2) = 3 - f(3)$ is equal to $.....$

Similar Questions

$A$ function $f: R - \{ 0 \} \rightarrow R$ is defined as $f(x) = \begin{cases} x^2 + 3x - 7, & x > 0 \\ h(x), & x < 0 \end{cases}$ If $f(x)$ is an odd function,then $h(x) =$

If $f(x) = |\sin x| + |\cos x|$ and $g(x) = [x]$,then what is the period of $h(x) = g(f(x))$,where $[.]$ denotes the Greatest Integer Function $(G.I.F.)$?

The function $f: R-\{1\} \rightarrow R-\{4\}$ defined by $f(x) = \frac{4x-3}{x-1}$ for $x \in R-\{1\}$ is

In each of the following cases,state whether the function is one-one,onto or bijective. Justify your answer. $f : R \rightarrow R$ defined by $f(x) = 3 - 4x$.

For $0 \leq x \leq 1$,what type of function is $f(x) = |x| + |x - 1|$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module