JAMIA 2024 — Mathematics PYQ
JAMIA | Mathematics | 2024A = {1,2,3} which of the following function f: A A does not have an inverse function
Choose the correct answer:
- A.
{(1,1), (2,2), (3,3)}
- B.
{(1,2), (2,1), (3,1)}
(Correct Answer) - C.
{(1,3), (3, 2), (2, 1)}
- D.
{(1,2), (2, 3), (3, 1)}
{(1,2), (2,1), (3,1)}
Explanation
Solution :
Ek function f:A→A ka inverse tabhi hota hai jab wo One-one (Injective) ho.
Diye gaye function mein:
Yahan hum dekh sakte hain ki:
Kyunki do alag-alag elements (2 aur 3) ki image same (1) hai:
Kyunki function One-one nahi hai, iska inverse f−1 define nahi kiya ja sakta.
Final Answer:
Function {(1,2),(2,1),(3,1)} ka inverse function nahi hai.
Explanation
Solution :
Ek function f:A→A ka inverse tabhi hota hai jab wo One-one (Injective) ho.
Diye gaye function mein:
Yahan hum dekh sakte hain ki:
Kyunki do alag-alag elements (2 aur 3) ki image same (1) hai:
Kyunki function One-one nahi hai, iska inverse f−1 define nahi kiya ja sakta.
Final Answer:
Function {(1,2),(2,1),(3,1)} ka inverse function nahi hai.