let f be one one function with domain {x,y,z} and range {1,2,3} it is given that exactly one of the - Maths - Relations and Functions

Question

let f be one one function with domain {x,y,z} and range {1,2,3}
it is given that exactly one of the following statement is true and
remaining two are false
f(x)=1,f(y)not equal to 1,f(z) not equal to 2 determine f
inverse(1)

Priyanka Kedia · Accepted Answer

Given that exactly one of the given statement is true and remaining two are false
Case1:Let fx=1 is true and fy≠1 and fz≠2 is false
⇒fx=1, fy=1,fz=2⇒f has a many one mapping
But, this contradict because f be one one function
Thus, case 1 is not possible
Case2:Let fy≠1 is true and fx=1 and fz≠2 is false
⇒fy≠1, fx≠1,fz=2⇒f has a many one mapping
But, this contradict because f be one one function
Thus, case 2 is not possible
Case3:Let fz≠2 is true and fx=1 and fy≠1 is false
⇒fz≠2, fx≠1,fy=1⇒fz=1,fx=2,fy=1⇒f has a one-one mapping
Now, fy=1⇒f-11=yThus, case 2 is not possible

let f be one one function with domain {x,y,z} and range {1,2,3}.it is given that exactly one of the following statement is true and remaining two are false. f(x)=1,f(y)not equal to 1,f(z) not equal to 2.determine f inverse(1)

let f be one one function with domain {x,y,z} and range {1,2,3}.it is given that exactly one of the following statement is true and remaining two are false.

f(x)=1,f(y)not equal to 1,f(z) not equal to 2.determine f inverse(1)