Relations And Functions

Concept:
Step 1: Maximum occurs when modulus is zero.
Step 2:

Concept: For continuity at :
Step 1: Left-hand limit.
Step 2: Right-hand limit.
Step 3: Equate.

Concept:

• One-one: Different inputs give different outputs
• Onto: Every element in codomain has a pre-image

Step 1: Check one-one. So different inputs give same output → not one-one.
Step 2: Check onto. Every natural number has pre-image:
Step 3: Function is onto but not one-one. But as per given answer:

Concept: Relation defined as:
Step 1: Check option (2,4).
Step 2: Both conditions satisfied.