CLASS 11 · FREE LEARNING CORNER

Functions, sequences & coordinate geometry

Build dependable school-level foundations before attempting harder JEE problems.

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Five questions. No timer, no registration. Keep a notebook nearby and show your working. This is a small practice snapshot, not a full assessment or rank prediction.

CLASS 11 · SAMPLE MODULE

Understand. Work it out. Check.

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One idea to remember

The domain of a real-valued function is the set of allowed inputs. A denominator cannot be zero. A quantity inside a real square root must be non-negative.

Worked example: Find the real domain of f(x) = √(x − 3).

For a real square root, the expression inside must be non-negative.
Therefore x − 3 ≥ 0, which gives x ≥ 3.
The domain is [3, ∞). The endpoint 3 is included because √0 is defined.

Your turn

Write your method before opening the answer. These original questions are for practice, not official past-exam papers.

1. What is the real domain of 1/(x − 4)?

Show answer & explanation

All real x except 4

The denominator cannot be zero, so x − 4 ≠ 0 and x ≠ 4. All other real values are allowed.

2. Find the sum 1 + 2 + 4 + 8 + 16.

Show answer & explanation

These are five GP terms with a = 1, r = 2. Sum = (2⁵ − 1)/(2 − 1) = 31.

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