CAT Functions and Domains Bible Top 10 Must Solve Functions and Domains Questions covering 90% of Syllabus
Every real CAT question on this chapter from the past papers we have, newest year first. Passages and data sets stay together on one page.
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Start here: the repeating CAT PYQs
Study the domain pattern in each CAT PYQ, then practise variations. The 14 selected families contain 52 of the 52 questions on Functions and Domains in the reviewed set.
CAT Functions and Domains Bible Top 10 PYQ Questions
| Questions | CAT Area Covered |
|---|---|
| First 5 CAT Questions | 69.23% |
| First 10 CAT Questions | 92.31% |
| All 14 CAT Questions | 100% |
Importance of Functions and Domains each year of CAT exam
| CAT year | Total Functions and Domains questions | First 6 examples | First 10 examples | All 14 examples | Outside these 14 families | Share of all Quant |
|---|---|---|---|---|---|---|
| 2021 | 15 | 13 | 15 | 15 | 0 | 22.73% |
| 2022 | 8 | 5 | 7 | 8 | 0 | 12.12% |
| 2023 | 13 | 9 | 12 | 13 | 0 | 19.70% |
| 2024 | 9 | 8 | 8 | 9 | 0 | 13.64% |
| 2025 | 7 | 5 | 6 | 7 | 0 | 10.61% |
| Total | 52 | 40 | 48 | 52 | 0 | 15.76% |
| Share of all 52 | 100% | 76.92% | 92.31% | 100% | 0% |
Quick review for beginners and last day revision
| Rule | Formula or what to do | Small example |
|---|---|---|
| Division | Every denominator must be nonzero. | 1/(x − 2) requires x ≠ 2. |
| Square root | A real square root requires its radicand ≥ 0. | √(x − 3) requires x ≥ 3. |
| Square root in a denominator | The radicand must be strictly positive. | 1/√(x − 3) requires x > 3. |
| Logarithm argument | The logarithm argument must be positive. | log(x − 2) requires x > 2. |
| Logarithm base | The base must be positive and different from 1. | logₓ(5) requires x > 0 and x ≠ 1. |
| Composition | The input must be allowed in the inner function and its output in the outer function. | For f(g(x)), check g first, then the conditions imposed by f. |
| Squaring | Squaring may introduce extra roots. Check the original equation. | √x = −2 has no real solution even though squaring gives x = 4. |
| Modulus branches | A solution must belong to the interval assumed for its signs. | If a case assumes x < 0, reject x = 3 from that case. |
| Physical quantities | Use the context restrictions on counts, speeds, volumes and time. | Reject a replacement volume larger than the vessel. |
| Ranges and limits | An approached limit is not automatically an attained value. | A range can be [3/7, 1/2), excluding 1/2. |
10 Core CAT PYQ Questions
Study these first.
CAT PYQ 1: Reject nonphysical roots in quantity and time problems
Understand: Solve the equation, then throw away any root that gives a negative or impossible count, time or volume.
Answer: 35
Solution — first steps
Step 2. Average difference gives 200/n−152/(n+21)=3.
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CAT PYQ 2: Logarithm base and argument restrictions
Understand: A logarithm needs a positive argument and a positive base that is not 1. Write the domain first, then solve.
Answer: 99
Solution — first steps
Step 2. Write every square-root log as half a log and multiply the equation by 2.
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CAT PYQ 4: Denominator zeros and composite or reciprocal inputs
Understand: Factor top and bottom, mark the zeros and the excluded points on a number line, then read off the sign.
Answer: A. \(-5 < x < -2\) or \(3 < x < 9\)
Solution — first steps
Step 2. Critical points−5, −2, 3, 9; poles−2, 9 are excluded.
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CAT PYQ 5: Radical arguments and square root signs
Understand: Square roots need a non-negative inside. Use the sum and the difference of the two roots to find each root.
Answer: D. \(3 \sqrt{7}\)
Solution — first steps
Step 2. Therefore A−B=18/[3(2+√2)]=3(2−√2).
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CAT PYQ 6: Exponential substitutions, zero bases and exponent conditions
Understand: Bound the exponent first, then check which whole-number values keep the expression an integer.
Answer: 7
Solution — first steps
Step 2. The requested values 3+3^(n+1) are integers only when n≥−1.
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CAT PYQ 7: Feasible output range of rational expressions
Understand: Put t = (x + 1)², which is at least 0, and see which values the expression reaches and which it only approaches.
Answer: D. \([\dfrac{3}{7}, \dfrac{1}{2})\)
Solution — first steps
Step 2. Function becomes(t+3)/(2t+7)=1/2−1/[2(2t+7)].
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CAT PYQ 8: Piecewise function or region interval membership
Understand: Check each branch of the function on its own, then combine the intervals where the condition holds.
Answer: B. x ≤ r
Solution — first steps
Step 2. For x≥r, f(x)=2x−r≥r.
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CAT PYQ 9: Positivity and nonzero roots in reciprocal identities
Understand: Since x is positive, build x^n + 1/x^n step by step from the smaller powers.
Answer: D. \(34 \sqrt{5}\)
Solution — first steps
Step 2. From A8=47, obtain A4=√49=7, A2=√9=3 and A1=√5.
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CAT PYQ 10: Select a difference using its given sign
Understand: Solve for the difference first, then use the given sign to pick the one valid answer.
Answer: D. 8
Solution — first steps
Step 2. Add the original equations: x²+y²−2xy−x+y=56.
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Variations
Same idea, extra twist.
CAT PYQ 11: Positive substitution needed for AM GM
Understand: Put t = 3 − x, which is positive, so the expression becomes t + 1/t and AM-GM gives the minimum.
Answer: B. 2
Solution — first steps
Step 2. Numerator x²−6x+10=(x−3)²+1=t²+1.
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If S represents all feasible values of x, then a possible subset of S is
Answer: D. (3, √10] ∪ [5, √26) ∪ {6}
Solution — first steps
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Answer: 0
Solution — first steps
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h(x) = f(g(x)) + g(f(x)) is all real numbers except
Answer: A. −1, 1, and 1/2
Solution — first steps
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Answer: A. (−∞, −3) ∪ (3, ∞)
Solution — first steps
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log_(x-3)(x² - 9) = log_(x-3)(x + 1) + 2 is :
Answer: C. (3+√33)/2
Solution — first steps
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Frequently asked questions
Where can I find CAT functions and domains questions with solutions?
Every Functions and Domains question on this page is a real CAT question from the CAT Actual Quant Papers. Tap Show answer for the answer; the detailed step-by-step solution opens after a free login. Start with the CAT PYQs at the top, because they repeat the most.
Are there CAT functions and domains questions with answers?
Yes. Every question has its answer one tap away, free for everyone: pick an option and press Submit, or tap Show answer.
Is there a PDF of CAT functions and domains questions?
Yes. Tap Download PDF at the top of this page (free, after a quick OTP login) for the CAT Functions and Domains Bible Top 10 PYQ Questions, a free PDF of the 10 most repeated CAT functions and domains questions. All the CAT Functions and Domains questions are also on this page to read online, with answers and, after a free login, detailed solutions.
What are the CAT functions and domains previous year questions (PYQs)?
They are the real questions of the CAT Actual Quant Papers that are about functions and domains: 52 questions, grouped into 14 repeating CAT PYQs, with the other questions listed after them in paper order.
Which functions and domains questions should I practise first for CAT?
Start with the first 6 CAT PYQs, which cover about 80% of the Functions and Domains questions. Then do the first 10 (about 90%) and finally all 14 (all of them).
How many Functions and Domains questions came in CAT papers?
39 Functions and Domains questions are on this page: 7 in CAT 2025, 11 in CAT 2024, 11 in CAT 2023, 6 in CAT 2022, 4 in CAT 2021. The same real question is shown once.
How difficult are CAT Functions and Domains questions?
Of the 7 Functions and Domains questions that carry a difficulty rating, 5 are Easy, 1 Medium and 1 Hard; the other 32 are not rated yet.
Are the solutions free?
The question and its answer are free for everyone. The detailed Cetking solution opens after a free login with your mobile number (OTP).
How is a set shown on this page?
Each passage or data set gets one page with all its questions together (4 sets here), so you never solve half of one. Questions that stand alone are shown five to a page.
Where can I practise more Functions and Domains?
Open all CAT papers and topics for every paper, or the Cetking Arena to practise.
Last day solving checklist
- Name the unknown. Include its unit and state whether it is a count, amount, rate or parameter.
- Form the relationships. Translate each given condition into an equation or restriction.
- Choose the method. Use the formula, substitution, elimination, a sign chart or a bound appropriate to this concept.
- Check restrictions. Check integer counts, signs, nonzero denominators, domains and all original conditions.
- Verify the answer. Substitute into the original question; for an extreme, show a feasible example reaches it.
All 14 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Reject nonphysical roots in quantity and time problems | 11 | CAT 2021 S1 Q16 | 11 | 21.15% |
| 2 | Logarithm base and argument restrictions | 10 | CAT 2021 S1 Q4 | 21 | 40.38% |
| 3 | Modulus branches and sign consistency | 6 | CAT 2021 S2 Q16 | 27 | 51.92% |
| 4 | Denominator zeros and composite or reciprocal inputs | 5 | CAT 2021 S1 Q1 | 32 | 61.54% |
| 5 | Radical arguments and square root signs | 4 | CAT 2023 S1 Q3 | 36 | 69.23% |
| 6 | Exponential substitutions zero bases and exponent conditions | 4 | CAT 2021 S2 Q15 | 40 | 76.92% |
| 7 | Feasible output range of rational expressions | 3 | CAT 2021 S2 Q13 | 43 | 82.69% |
| 8 | Piecewise function or region interval membership | 2 | CAT 2022 S3 Q6 | 45 | 86.54% |
| 9 | Positivity and nonzero roots in reciprocal identities | 2 | CAT 2023 S3 Q4 | 47 | 90.38% |
| 10 | Select a difference using its given sign | 1 | CAT 2021 S2 Q3 | 48 | 92.31% |
| 11 | Positive substitution needed for AM GM | 1 | CAT 2022 S3 Q2 | 49 | 94.23% |
| 12 | Given work time interval | 1 | CAT 2023 S3 Q8 | 50 | 96.15% |
| 13 | Select the negative shared root | 1 | CAT 2024 S1 Q20 | 51 | 98.08% |
| 14 | Open and closed floor band endpoints | 1 | CAT 2025 S1 Q22 | 52 | 100% |
Based on CAT Actual Quant Papers.