Q2 of 99 Page 53

Prove that the function f: N → N : f (x)=3x is one-one and into.

To prove: function is one-one and into


Given: f: N → N : f(x)= 3x


We have,


f(x) = 3x


For, f(x1) = f(x2)


⇒ 3x1 = 3x2


⇒ x1 = x2


When, f(x1) = f(x2) then x1 = x2


∴ f(x) is one-one


f(x) = 3x


Let f(x) = y such that


⇒ y = 3x



If y = 1,



But as per question , hence x can not be


Hence f(x) is into


Hence Proved


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