Q. 2 C4.3( 37 Votes )

# Check the injectivity and surjectivity of the following functions:

f : R → R given by f (x) = x^{2}

Answer :

It is given that f : R → R given by f (x) = x^{2}

We can see that f(-1) = f(1) = 1, but -1 ≠ 1

⇒ f is not injective.

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

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

⇒ f is not surjective.

Therefore, function f is neither injective nor surjective.

Rate this question :

Fill in the blanks in each of the

Let the relation R be defined in N by aRb if 2a + 3b = 30. Then R = ______.

Mathematics - ExemplarFill in the blanks in each of the

Let the relation R be defined on the set

A = {1, 2, 3, 4, 5} by R = {(a, b) : |a^{2} – b^{2}| < 8}. Then R is given by _______.

State True or False for the statements

Every relation which is symmetric and transitive is also reflexive.

Mathematics - ExemplarState True or False for the statements

Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.

Mathematics - Exemplar