The function f: N → N defined by f(x) = x - 5 [ (x/5) ], where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is :

Question

The function f: N → N defined by f(x) = x - 5 [ (x/5) ], where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is : (A) not a function (B) one-one but not onto. (C) onto but not one-one. (D) neither one-one nor onto.

Tardigrade Admin · Accepted Answer

f (10)=10-5(2)=0 which is not in co-domain.

Q. The function $f : N \to N$ defined by $f (x) = x - 5 [\frac{x}{5}]$ , where $N$ is the set of natural numbers and $[x]$ denotes the greatest integer less than or equal to $x$ , is :

not a function

one-one but not onto.

onto but not one-one.

neither one-one nor onto.

$f (10) = 10 - 5 (2) = 0$ which is not in co-domain.

Q. The function f:N→N defined by f(x)=x−5[5x​], where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is :