The function f : N [ ] N defined by f (x) = x - 5 [[ x 5 ],] Where N is the set of natural…

Question

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

Accepted Answer

f(1) = 1 - 5$$\left[ {{1 \over 5}} \right]$$ = 1

f(6) = 6 - 5$$\left[ {{6 \over 5}} \right]$$ = 1

So, this function is many to one.

f(10) = 10 - 5$$\left[ {{10 \over 5}} \right]$$ = 0 which is not present in the set of natural numbers.

So this function is neither one-one nor onto.

Solutions · 1