Question

✌✌✌✌✌hi guys .

if f :N to N is defined as f(x) = x^2the images of 1 and 2 are ________ and__________.
give correct answer☠☠☠ don't waste my time by typing something else☠☠☠​

Answer 1

Hie!!

Given Function is

F: N ➡️N

F(x) = x²

Here Domain , Range and codomain of this Function is set of natural numbers.

Elements belonging to the codomain are the mirror images of Elements belonging to the Domain.

F(x) = x²

For x = 1 we have it's image as

F(1) = 1²

F(1) = 1

For x = 2 , we have it's image as

F(2) = 2²

F(2) = 4

So, The images of 1 and 2 are 1 and 4 Respectively.

Pre image of 1 and 2 is

1 = x²

x = 1 OR x = -1

And

2 = x²

x = √2 OR x = -√2

So, The pre image of 1 and 2 are 1 and √2 respectively.

Note:- -1 and -√2 will be rejected becoz domain is set of Natural numbers.

Answer 2

If f:N to N be defined by f(x)= x².

Then "f" is an injection since for a1, a2€N and

f(a1) = f(a2) = a1²=a2² = (a1²-a2²) = 0

= (a1-a2) (a1+a2)= 0

=a1-a2=0 [:;a1,a2€N= a1+a2>0] = a1=a2.

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