u. Prove that the functionf:N N defined by fw)N defined by fx) 3x 2 is

1.	u. Prove that the functionf:N N defined by fw)N defined by fx) 3x 2 is one-one but not ont3t-2 is one-one but not ondtion f: NHint. 2 has no pre-image in
Answer» Given : f(x) = 3x - 2 One - one proof Let x and y belongs to NSo, if f(x) = f(y) we will show x = y 3x - 2 = 3y - 2 3x = 3y x = y so f is one one. Now, we it is not onto Use hint let f(x) = 2 So, 3x - 2 = 2 So, 3x = 4 x = 4/3 But the set is only restricted to N set and 4/3 is from rational set so we can't get 2 using N set so it not onto

u. Prove that the functionf:N N defined by fw)N defined by fx) 3x 2 is one-one but not ont3t-2 is one-one but not ondtion f: NHint. 2 has no pre-image in

Answer»

Given : f(x) = 3x - 2

One - one proof

Let x and y belongs to NSo, if f(x) = f(y) we will show x = y

3x - 2 = 3y - 2

3x = 3y

x = y so f is one one.

Now, we it is not onto

Use hint let f(x) = 2

So, 3x - 2 = 2

So, 3x = 4

x = 4/3

But the set is only restricted to N set and 4/3 is from rational set so we can't get 2 using N set so it not onto