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Question : 27
Total: 50
Let X = { x 2 : x ∈ N } f : N → X f ( x ) = x 2 , x ∈ N
Solution: 👈: Video Solution
Explanation: Let x 1 , x 2 ∈ N
f ( x 1 ) = f ( x 2 )
⇒ x 1 2 = x 2 2
⇒ x 1 2 − x 2 2 = 0
⇒ ( x 1 + x 2 ) ( x 1 − x 2 ) = 0
⇒ x 1 = x 2
Hence,f ( x )
Also, the elements like 2 and 3 have no pre-image in N. Thus,f ( x )
Hence,
Also, the elements like 2 and 3 have no pre-image in N. Thus,
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