Question

Match List - I with List - II. 

List - I		List - II
A.	Injective function	I.	\(f(x) = x^2\) on \(\mathbb{R}\)
B.	Surjective function	II.	\(f(x) = 2x + 3\) on \(\mathbb{R}\)
C.	Bijective function	III.	\(f(x) = x^3\) on \(\mathbb{R}\)
D.	Non-injective and non-surjective	IV.	Every element of a codomain has a preimage

Choose the correct answer from the options given below:

• A. A-I, B-III, C-II, D-IV
• B. A-III, B-I, C-IV, D-II
• C. A-II, B-IV, C-III, D-I
• D. A-II, B-IV, C-I, D-III

Hint:

On $\mathbb{R}$, $x^2$ is the classic example of a "bad" function: it fails the Horizontal Line Test twice!

Answer 1

The Correct Option is C

We match mathematical definitions of functions with their properties and examples on the set of Real numbers ($\mathbb{R}$). 1. Injective Function (A-II): An injective (one-to-one) function means $f(a)=f(b) \implies a=b$. $f(x)=2x+3$ is a linear function; every distinct input gives a distinct output. 2. Surjective Function (B-IV): By definition, a surjective (onto) function is one where the Range equals the Codomain, meaning every element of the codomain has at least one preimage. 3. Bijective Function (C-III): A bijection is both injective and surjective. $f(x)=x^3$ on $\mathbb{R}$ is bijective because it covers all real values (surjective) and preserves distinctness (injective). 4. Non-injective and Non-surjective (D-I): $f(x)=x^2$ on $\mathbb{R}$ is not injective (since $f(-2)=f(2)=4$) and not surjective (since it can never produce negative values).