Verified Solution • 2025–26 Session moderate

QJEEM17Maaf16: JEE Main 2017 Mathematics - Class 11 JEEM17Maaf16 Solution: The function f : N N defined by f (x) = x 5 Where N is the set…

The function f : N →\to N defined by f (x) = x −- 5 [x5],\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 :

Multiple Choice Options

  • A one-one and onto
  • B one-one but not onto.
  • C onto but not one-one.
  • D neither one-one nor onto.

Step-by-Step Verified Solution

f(1) = 1 - 5 [15]\left[ {{1 \over 5}} \right] = 1

f(6) = 6 - 5 [65]\left[ {{6 \over 5}} \right] = 1

So, this function is many to one.

f(10) = 10 - 5 [105]\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.

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