Class 12 Math: Relations and Functions Solved Examples & Step Solutions

The best way to gain confidence in mathematics is by studying solved examples. By analyzing how formulas are applied step-by-step, you learn how to tackle complex questions in your homework and exams. Let's walk through standard worked examples for Class 12 Relations and Functions.

Step-by-Step Solved Problems

Example 1: Bijective Function verification

Worked Solution Steps:

1. Check injection (one-to-one): If f(x1) = f(x2) => 3 - 4x1 = 3 - 4x2 => -4x1 = -4x2 => x1 = x2. It is injective.
2. Check surjection (onto): Let y in R. Equate y = 3 - 4x => 4x = 3 - y => x = (3-y)/4. Since x is always real for any real y, it is surjective.
3. Since it is both, it is bijective.

Self-Practice Method

When studying these examples, cover the solution with a sheet of paper and attempt to solve the question on your own. If you get stuck, reveal the steps one by one to identify where your logic deviated. This active recall method builds long-term problem-solving skills.