IEMJEE Maths preparation: One-to-one functions — concept guide

What one-to-one functions means

An injective function assigns different outputs to different allowed inputs. The choice of domain matters.

The working rule

Test whether f(a)=f(b) forces a=b within the stated domain.

Read each symbol or named operation in its stated context. Before using this rule, identify the input information and the output the question actually requests. A rule recalled from memory still needs its domain and assumptions.

Set up a valid model

Write the domain, any nonzero-denominator conditions and the exact quantity requested. A correct algebraic manipulation must still respect those restrictions. Exact fractions and symbols are preferable until a decimal approximation is specifically useful.

Distinction to understand

A graph passing the vertical-line test is a function, but it need not be one-to-one.

Explain the distinction in your own words before moving to calculation. A useful explanation identifies which assumption or reference convention would have to change for a different answer to become appropriate.

Check your understanding

Without computing a new numerical case, explain why this statement is relevant: Test whether f(a)=f(b) forces a=b within the stated domain.

Substitute a candidate result into the original statement where possible. Inspect sign, endpoint inclusion and whether a real or complex answer is requested. The simplified expression and the original expression can have different domains even when their nearby values agree.

Continue with a deliberate learning sequence

The worked example shows one complete application. The worksheet provides a different question and a related-skill transfer task. The error clinic then asks you to diagnose a plausible wrong approach. These are separate learning activities; completion is not a prediction of an examination score.

Official sources and verification

Sources checked on 26 October 2026. A source’s date, programme and campus limit which claims it supports. Official pages may change after review.

1. UEM — IEMJEE examination information

   Historical examination pattern; verify the current cycle on the central portal.

2. NTA — explicitly labelled JEE Main 2026 syllabus

   Historical PCM syllabus reference. Lessons and exercises are independently authored, not official IEMJEE papers or verified 2027 paper predictions.

3. NCERT — official textbook catalogue

   Primary textbook reference for checking school-level concepts. This directory does not certify the independent lesson or establish IEM examination weightage.

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