What are function questions in CAT 2025 Quant?

Function questions test your understanding of domains, ranges, inverses, and composite functions in the Quantitative Aptitude section.

How many function questions appear in CAT 2025?

Usually, 2 – 3 function-based questions are asked in CAT 2025 Quant, often mixed with algebra or graph-based problems.

Which formulas are important for CAT function questions?

Formulas for linear, quadratic, and rational functions, along with composite and inverse function rules, are crucial for CAT 2025.

How can I prepare for function questions in CAT 2025?

Start by understanding domain-range basics, then practice composite and inverse problems from topic-wise CAT Quant PDFs.

Are function questions tough in CAT?

They are moderate to tricky, but with clear conceptual understanding and formula revision, they become scoring topics.

What are common mistakes in CAT function questions?

Ignoring domain restrictions, mixing domain & range, and misapplying inverse operations are common mistakes to avoid.

Where can I download CAT function formulas PDF?

You can download the free CAT Functions Formula PDF from Cracku’s website to revise all key rules and examples.

Why are function questions important for CAT Quant 2025?

Functions build your algebraic reasoning and appear regularly in CAT, helping you strengthen conceptual problem-solving skills.

Most Important Function Questions For CAT 2025 with Solutions

Latest Updates:

October 25, 2025: Here we have discussed the XAT 2026 important topics and section-wise weightage, including must-study chapters like Algebra, Critical Reasoning, and Current Affairs.Read More
October 25, 2025: Here we have discussed FMS Delhi Summer Placements 2026 with detailed sector-wise report, stipend statistics, and top recruiters driving 100% placement success.Read More

Download PDF

Function Questions For CAT  2025

Function questions are a frequent topic in the CAT Quant section. They test your understanding of how functions work, domains, ranges, composite functions, inverses, and transformations. In CAT 2025, you can expect both straightforward and tricky function problems. Below are some of the most important types of function questions you should practise to become comfortable with them.

Download CAT Function Questions PDF

Important Formulas for CAT Function Questions

To solve function questions easily in CAT, you should remember the key formulas and rules related to functions. These formulas help you work with domains, ranges, composite functions, inverses, and transformations quickly. They save time, reduce mistakes, and make even tricky function problems easier to handle. With regular practice, you’ll improve both your speed and accuracy in this topic.

Download CAT Functions Formula PDF

Concept	Formula / Rule	Explanation / Use
Basic (Linear) Function	f(x) = ax + b	Straight-line graph; slope a, intercept b
Quadratic Function	f(x) = ax² + bx + c Vertex: x = -b / (2a)	Parabolic curve; opens up or down
Cubic Function	f(x) = ax³ + bx² + cx + d	S-shaped (sigmoidal) curve
Rational Function	f(x) = (ax + b) / (cx + d)	May have vertical/horizontal asymptotes
Composite Function	f(g(x))	Apply g(x) first, then f(x)
Inverse Function	f(f⁻¹(x)) = x and f⁻¹(f(x)) = x	Inverse reverses the function
Domain Rule	Denominator ≠ 0, √expression ≥ 0	Determines valid input values
Range Rule	Find from domain or use inverse	Describes possible output values
Even Function	f(−x) = f(x)	Symmetric about y-axis
Odd Function	f(−x) = −f(x)	Symmetric about origin
Horizontal Shift	f(x + c)	Shifts graph left by c units
Vertical Shift	f(x) + c	Shifts graph up by c units
Stretch / Shrink	f(cx) → horizontal c·f(x) → vertical	Stretches or compresses the graph
Piecewise Function	Defined by different rules for intervals	Function depends on input range
Absolute Value Function	f(x) = \|x\|	Output is always non-negative
Greatest Integer Function	f(x) = ⌊x⌋	Rounds x down to nearest integer
Signum Function	f(x) = { 1 if x > 0, 0 if x = 0, −1 if x < 0 }	Indicates the sign of the input

Common Mistakes to Avoid in CAT Function Questions

While solving function problems, students often make avoidable mistakes. Here are some common ones to watch for:

Assuming the type wrongly: A function may look linear but has hidden domain restrictions.
Mixing up domain & range: Always check valid xxx values first before jumping to outputs.
Neglecting composite order: In f(g(x))f(g(x))f(g(x)), you must compute g(x)g(x)g(x) first, then apply fff.
Wrong inverse operations: Mistakes in algebra when finding f−1(x)f^{-1}(x)f−1(x) are frequent.
Overlooking piecewise parts: If a function is defined piecewise, ensure you're using the correct piece for the input.
Ignoring transformation impact: For f(x+c)f(x + c)f(x+c) or f(cx)f(cx)f(cx), wrong shifts or stretches often lead to errors.

List of CAT Function Questions

Question 1

Let $$f(x) = ax^2 + bx + c$$, where a, b and c are certain constants and $$a \neq 0$$ ?

It is known that $$f(5) = - 3f(2)$$. and that 3 is a root of $$f(x) = 0$$.

What is the other root of f(x) = 0?

Show Answer Explanation Video Solution

Question 2

The area of the region satisfying the inequalities $$\mid x\mid-y\leq1,y\geq0$$ and $$y\leq1$$ is

Show Answer Explanation Video Solution

Question 3

Let g(x) be a function such that g(x+1) + g(x-1) = g(x) for every real x. Then for what value of p is the relation g(x+p) = g(x) necessarily true for every real x?

Show Answer Explanation Video Solution

Instruction for set :

DIRECTIONS for the following questions: These questions are based on the situation given below: In each of the questions a pair of graphs F(x) and F1(x) is given. These are composed of straight-line segments, shown as solid lines, in the domain $$x\epsilon (-2, 2)$$.

choose the answer as

a. If F1(x) = - F(x)

b. if F1(x) = F(- x)

c. if F1(x) = - F(- x)

d. if none of the above is true

Question 4

Show Answer Explanation

Question 5

Suppose for any real number x, [x] denotes the greatest integer less than or equal to x. Let L(x, y) = [x] + [y] + [x + y] and R(x, y) = [2x] + [2y]. Then it is impossible to find any two positive real numbers x and y for which