Q. 2 E4.1( 28 Votes )

# Check the injecti

Answer :

It is given that f : Z → Z given by f (x) = x^{3}

We can see that for x, y ϵ N,

f(x) = f(y)

⇒ x^{3} = y^{3}

⇒ x = y

⇒ f is injective.

Now, let 2 ϵ Z. But, we can see that there does not exists any x in Z such that

f(x) = x^{3} = 2

⇒ f is not surjective.

Therefore, function f is injective but not surjective.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

Fill in theMathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

State True Mathematics - Exemplar

Let A = {1, 2, 3}Mathematics - Exemplar

Show that the relMathematics - Board Papers

Let N denote the Mathematics - Board Papers