Q Show that the function f : N→N, defined by f (x) = 2x, is one-one but not onto - Maths - Relations and Functions

Question

Q Show that the function f   :   N → N , defined by
f (x) = 2x, is one-one but not onto

Amit Shukla · Accepted Answer

Dear Student,

We have,f(x)=2xNow, for one-onef(x1)=2x1f(x2)=2x2Putting f(x1)=f(x2)2x1=2x2x1=x2Therefore,If f(x1)=f(x2) then, x1=x2So,the function is one-oneAnd for Onto;f(x)=2xLet f(x)=y, such that y∈N2x=yx=y2So, if y=1then, x=12=0
5, which is not possible as x∈Ntherefore, the function is not onto

Regards

Q. Show that the function f : N → N , defined by f (x) = 2x, is one-one but not onto.

Q. Show that the function $f : N \to N$ , defined by f (x) = 2x, is one-one but not onto.