Let A - 0- 1- 2- 3- 4- 5- 6- 7- Then the number of bijective functions f-A- A such that f1 - f2 - 3 - f3 is equal to

F(1) + f(2) = 3 f(3) ⇒ f(1) + f(2) +f(3)= 3 The only possibility is 0+1+2=3 ⇒ Elements 1, 2, 3 in the domain can be mapped with 0, 1, 2 only. ∴ Total number ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Condition for Monotonically Decreasing Function

Let A = 0, 1,...

Question

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

720.0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

720

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

720.00

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

$f (1) + f (2) = 3 - f (3)$
$\Rightarrow f (1) + f (2) + f (3) = 3$
The only possibility is $0 + 1 + 2 = 3$
$\Rightarrow$ Elements $1, 2, 3$ in the domain can be mapped with $0, 1, 2$ only.

$∴$ Total number of bijective functions $= 5! 3! = 720$

Suggest Corrections

Similar questions

Q. Let

A = {x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}}

and

f : A \to A

. The number of bijective functions such that

f (x_{i}) \neq x_{i}

for exactly

3

elements

(i = 1 to 6)

Q. Let

f (x)

is a cubic polynomial such that

f (1) = 1, f (2) = 2, f (3) = 3

and

f (4) = 16

, then

f (0)

is equal to

Q. If

f : Z \to Z

be a linear function such that

f (2) + f (1) = 4, f (2) - 2 f (1) = - 1

, then

f (3)

Q. Let

f (x)

be an even function & even degree polynomial such that

f (\begin{matrix} \frac{1}{2} \end{matrix}) = \frac{1}{2}, f (1) = 1, f (2) = - 3, f (3) = 5

then minimum number of points of intersection for

f (x)

Q. Let

f (x)

be a differentiable function on

[0, 8]

such that

f (1) = 6, f (2) = \frac{1}{3}, f (3) = 8, f (4) = - 2, f (5) = 5, f (6) = \frac{1}{5}, and f (7) = - \frac{1}{3}

If the minimum number of roots of the equation

f^{'} (x) - f^{'} (x) (f (x))^{2} = 0 is λ then \frac{λ}{11}

Join BYJU'S Learning Program

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

f(1)+f(2)=3−f(3) ⇒f(1)+f(2)+f(3)=3 The only possibility is 0+1+2=3 ⇒ Elements 1,2,3 in the domain can be mapped with 0,1,2 only. ∴ Total number of bijective functions =5!3!=720

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

$f (1) + f (2) = 3 - f (3)$
$\Rightarrow f (1) + f (2) + f (3) = 3$
The only possibility is $0 + 1 + 2 = 3$
$\Rightarrow$ Elements $1, 2, 3$ in the domain can be mapped with $0, 1, 2$ only.

$∴$ Total number of bijective functions $= 5! 3! = 720$