Which of the following statements correctly defines an injective (one-one) function ?

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Which of the following statements correctly defines an injective (one-one) function

f:A\to B

? (a) For every

y\in B

, there exists at least one

x\in A

such that

f(x)=y

.},{ (b) For every

x\in A

, there exists a unique

y\in B

such that

f(x)=y

.},{ (c) If

f(x_1)=f(x_2)

, then

x_1=x_2

for all

x_1,x_2\in A

.},{ (d) The function has an inverse satisfying

f^{-1}\circ f=I_A

and

f\circ f^{-1}=I_B

.}],