Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2024MathematicsFunctions

Let: f: N N be defined as f(n)= array ll n+1 2 , & if is n odd n 2 , & if n is even array . for all n N . Then f is

Options

  1. Ainjective but not surjective
  2. Bsurjective but not injective
  3. Cboth injective and surjective
  4. Dneither injective nor surjective

Correct answer

B. surjective but not injective

Step-by-step solution

f(n)= cases n+1 2 , & n is odd n 2 , & n is even cases f(1)= 1+1 2 =1 and f(2)= 2 2 =1 f(1)=f(2)=1 So, f is not injective and Range of f(n) is all natural numbers. So, it is surjective Hence, f is surjective but not injective.

Practice Functions on Quantrex Academy →

More from Functions

If f : R A , defined by f ( x )= x + 3 x -1 , is an onto function then A = 2025Let g(x)=1+x-[x] and f(x)= cases -1, & x 0 cases ([x] ) denotes the greatest integer less than or equal to (x ). Then for all x , f ( g ( x ))= 2025The domain of the real valued function f(x)= 3 4-x^2 + ₁₀ (x^3-x ) is 2025A real valued function f: A B defined by f(x)= 4-x^2 4+x^2 x A is a bijection. If -4 A then A B= 2025Let [ x ] represent the greatest integer less than or equal to x , x = x -[ x ] , 2 =1.414 and 3 =1.732 . If f(x)= x+ [ x 1+x^2 ] is a real valued function, then f ( 2 )+ f (- 3 )= 2025If the range of the function f(x)=-3 x-3 is 3,-6,-9,-18 , then which one of the following is not in the domain of f ? 2025The domain of the function f(x)= _e ( 1 x^2-4 x+4 ) + ⁻¹ (x^2-2 ) is 2025Consider the following statements Statement-I : A function f : A B is said to be one-one if and only if f(x) f(y) x y Statement-II : A relation f: A B is said to be a function if x 2025 Full Functions list All Manipal MET PYQs