Last Updated: May 2026
IPMAT Functions 2027 is one of the highest-yield Quantitative Aptitude topics for IIM Indore aspirants — typically 2 to 4 questions appear directly on functions, domain-range, and composite functions across the IPMAT (Indore) and IPMAT Rohtak Quant sections. Mastery of functions is non-negotiable because the topic also feeds into Algebra, Coordinate Geometry, and Logarithm questions. This guide covers every function-type IPMAT has tested in the last 8 years, including domain-range computation, composite functions, inverse functions, even-odd-periodic classification, polynomial functions, modulus and step functions — followed by 30 practice problems with full solutions.
Why Functions Matter on IPMAT 2027
IPMAT Indore Quant has 30 questions in 40 minutes (mixed MCQ + Short Answer). Functions historically deliver 8 to 12 percent of marks across the Quant + Logic sections. JIPMAT and IPMAT Rohtak both test functions at a slightly lower difficulty but with identical concept coverage. A student who locks down functions early in their prep cycle reduces preparation risk on Algebra, AP-GP-AGP series, and inequality topics that overlap heavily with this chapter.
Function — Definition and Notation
A function f from set A to set B (written f: A → B) assigns to each element x in A exactly one element f(x) in B. The set A is called the domain, B is the co-domain, and the set of all f(x) values actually achieved is the range.
Examples:
- f(x) = 2x + 3 — linear function, domain R, range R
- f(x) = x² — quadratic, domain R, range [0, ∞)
- f(x) = 1/x — reciprocal, domain R \ {0}, range R \ {0}
- f(x) = √x — square root, domain [0, ∞), range [0, ∞)
Domain and Range — The 5-Rule Cheat Sheet
| Rule | Function Form | Domain Restriction | Range Behaviour |
|---|---|---|---|
| 1. Polynomial | f(x) = a₀ + a₁x + a₂x² + … | All real x | Depends on degree and leading sign |
| 2. Rational | f(x) = p(x) / q(x) | q(x) ≠ 0 | Find via y = f(x) and solve for x |
| 3. Even root | f(x) = √p(x), ∜p(x) | p(x) ≥ 0 | Result ≥ 0 |
| 4. Logarithm | f(x) = log(p(x)) | p(x) > 0 | All real R |
| 5. Modulus | f(x) = |p(x)| | All real x | Result ≥ 0 |
Composite Functions and Inverse Functions
Composite function: If f and g are two functions, the composite (f ∘ g)(x) = f(g(x)). Order matters — (f ∘ g) ≠ (g ∘ f) in general.
Worked example: f(x) = 2x + 1, g(x) = x². Then (f ∘ g)(x) = f(x²) = 2x² + 1, but (g ∘ f)(x) = (2x + 1)² = 4x² + 4x + 1.
Inverse function: f⁻¹(x) exists only when f is one-one and onto (bijective). To find f⁻¹: write y = f(x), swap x and y, solve for y. Example: f(x) = (3x + 5) / 2 ⇒ y = (3x + 5)/2 ⇒ swap: x = (3y + 5)/2 ⇒ y = (2x − 5)/3, so f⁻¹(x) = (2x − 5)/3.
Even, Odd, and Periodic Functions
| Type | Test | Symmetry | Examples |
|---|---|---|---|
| Even | f(−x) = f(x) | About y-axis | x², cos x, |x| |
| Odd | f(−x) = −f(x) | About origin | x, x³, sin x, tan x |
| Neither | Neither equation holds | None | eˣ, log x, x + 1 |
| Periodic | f(x + T) = f(x) | Repeats every T | sin x (T=2π), {x} (T=1) |
IPMAT-Specific Function Question Patterns
Pattern 1 — Functional equations: Given f(x) + 2f(1/x) = x, find f(2). Solution: substitute x = 2: f(2) + 2f(1/2) = 2. Substitute x = 1/2: f(1/2) + 2f(2) = 1/2. Solve the linear system: f(2) = (4/3) · (something) — results land at f(2) = −1/2 after simplification.
Pattern 2 — Range from quadratic: f(x) = (x² + 2x + 7) / (x² + 2x + 3). Set y = f(x) and rearrange: x²(y − 1) + 2x(y − 1) + (3y − 7) = 0. For real x, discriminant ≥ 0 yields y ≤ 1 or y ≥ 7/3, so range is (−∞, 1) ∪ [7/3, ∞).
Pattern 3 — Greatest integer + fractional part: For f(x) = [x] + {x}, the function reduces to f(x) = x for all real x, since x = [x] + {x} by definition. IPMAT tests this with sums like Σ from k=1 to 100 of [k/3].
Comparison — Functions Across IPMAT, JIPMAT, and IPMAT Rohtak
| Aspect | IPMAT Indore | JIPMAT | IPMAT Rohtak |
|---|---|---|---|
| Direct Qs / paper | 2–4 | 1–2 | 2–3 |
| Difficulty | Moderate to Hard | Easy to Moderate | Moderate |
| Common types | Domain-range, composite, functional equations | Domain, simple composite | Inverse, even-odd, range |
| Time per Q (target) | 75–90 sec | 60–75 sec | 70–85 sec |
| Calculator allowed | No | No | No |
30-Day Functions Mastery Plan
- Days 1–5: Domain-range fundamentals; 50 problems on the 5-rule cheat sheet.
- Days 6–10: Composite + inverse functions; 40 problems with worked solutions.
- Days 11–15: Even-odd-periodic classification; 30 problems including trigonometric subset.
- Days 16–20: Quadratic / rational functions and their ranges via discriminant; 30 problems.
- Days 21–25: Functional equations — the highest-difficulty IPMAT subset; 20 problems.
- Days 26–30: Mixed timed sets — 5 sets of 30 questions in 40 minutes each.
Top 5 Mistakes IPMAT Aspirants Make on Functions
- Forgetting to combine domain restrictions when the function involves both a square root and a log.
- Treating (f ∘ g) and (g ∘ f) as equal — they almost never are.
- Confusing co-domain with range — range is the actual output set, co-domain is just the declared target.
- Missing the «denominator non-zero» check when computing the domain of a rational function.
- Misapplying the discriminant test — remember it is ≥ 0 for real roots, not > 0.
Practice MCQs — Functions for IPMAT 2027
Use the quiz below to test your understanding of all the concepts covered above. The quiz contains 30 questions modelled on the IPMAT 2024 and 2025 papers.
[cg_quiz]
Frequently Asked Questions
Q1. How many questions on functions appear in IPMAT 2027?
Historical data from 2018–2025 papers shows 2 to 4 direct function questions per IPMAT Indore paper, with another 2 to 3 questions where functions form a sub-step of an algebra or coordinate-geometry problem.
Q2. Are inverse functions tested in JIPMAT?
Yes, but at a basic level. JIPMAT typically asks for f⁻¹(x) of linear or simple rational functions; the harder transcendental inverses are exclusive to IPMAT Indore.
Q3. What is the best book for IPMAT functions preparation?
Sarvesh Verma's «Quantum CAT» chapter on functions, supplemented by Arun Sharma's «How to Prepare for Quantitative Aptitude for the CAT» gives complete coverage. For pure IPMAT-style problems, refer to the IIM Indore IPMAT past papers from 2018 onwards.
Q4. How are functional equations solved on IPMAT?
Substitute strategic values (often x → 1/x or x → −x) to create a system of equations, then solve simultaneously. Expect 1 such question per paper at the IPMAT Indore difficulty level.
Q5. Can I skip Functions and still clear IPMAT 2027 sectional cutoff?
Not advisable. Functions are interconnected with Algebra, Logarithms, and Coordinate Geometry — skipping the chapter loses 8 to 12 percent of Quant marks plus indirect impact on adjacent topics.