How many Functions questions come in CAT Quant?

About 0.8 questions in a 22-question Quant section, worth roughly 2 marks. Functions appeared in 20 of the 24 CAT papers from 2017 to 2025, 23 questions in all, which ranks it 15 of 25 Quant chapters.

Are Functions questions in CAT MCQ or TITA?

48% of the Functions questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.

What types of Functions questions does CAT ask?

CAT keeps returning to 6 question shapes in Functions: A functional equation; Composition, evaluated or minimised; A substitution or symmetry trick; The greatest-integer function; Min or max of two curves, or a piecewise rule; Range or domain of a rational function.

Functions for CAT: Formulas, Weightage & Question Types

Functional equations, composition, greatest-integer and min-max of two curves.

Functions formula sheet

Everything CAT needs from Functions, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place.

Composition


Meaning	$(f \circ g)(x) = f(g(x))$ — inner function first
Order	$f(g(x)) \neq g(f(x))$ in general
Domain of $f(g(x))$	$x$ must be allowed in $g$ , and $g(x)$ must be allowed in $f$

Functional equations and what they force


$f(x+y) = f(x)f(y)$	$f(x) = a^x$ , so $f(n) = f(1)^n$
$f(xy) = f(x)f(y)$	multiplicative; always $f(1) = 1$ (or 0)
$f(x+y) = f(x) + f(y)$	$f(x) = cx$
$f(x) + k\,f\!\left(\frac{1}{x}\right) = g(x)$	write it again with $x \to \frac{1}{x}$ and solve the two together
$f(x+2) = f(x) + f(x+1)$	a recurrence — step forward from two known values
$f(xy) = f(x)f(y) + f(x) + f(y)$	set $g = f+1$ ; then $g$ is multiplicative

Useful substitutions


$x = y = 1$	pins down $f(1)$
$y = x$	turns a two-variable law into one variable
$x \to \frac{1}{x}$	pairs with the original to eliminate the unwanted term
A prime factorisation	a multiplicative $f$ is determined by its values on primes

Symmetry


$f(a+x) = f(a-x)$ for all $x$	the graph is symmetric about $x=a$
So the roots pair up	each pair sums to $2a$
With $2k$ roots	their total is $2ak$

The larger or smaller of two curves


$\min\{u(x), v(x)\}$	its maximum sits where the two curves cross
$\max\{u(x), v(x)\}$	its minimum sits where they cross
Either way	solve $u(x) = v(x)$ and substitute

Range of a rational function


Method	set $y = \dfrac{\text{num}}{\text{den}}$ , cross-multiply into a quadratic in $x$
Then	real $x$ needs discriminant $\ge 0$ — that inequality is the range
Alternative	substitute for a repeated block and track what it can be

Greatest integer, $[x]$


Meaning	the largest integer not exceeding $x$
So	$[x] = n \iff n \le x < n+1$
Summing $[\,\cdot\,]$ over a range	group the terms that share a value, then count each group
$\lfloor\sqrt{n}\rfloor = k$	for the $2k+1$ values $n = k^2$ to $k^2+2k$

The 6 Functions question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

01
A functional equation
02
Composition, evaluated or minimised
03
A substitution or symmetry trick
04
The greatest-integer function
05
Min or max of two curves, or a piecewise rule
06
Range or domain of a rational function

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Functions in CAT: quick answers

How many Functions questions come in CAT Quant?: About 0.8 questions in a 22-question Quant section, worth roughly 2 marks. Functions appeared in 20 of the 24 CAT papers from 2017 to 2025, 23 questions in all, which ranks it 15 of 25 Quant chapters.
Are Functions questions in CAT MCQ or TITA?: 48% of the Functions questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Functions questions does CAT ask?: CAT keeps returning to 6 question shapes in Functions: A functional equation; Composition, evaluated or minimised; A substitution or symmetry trick; The greatest-integer function; Min or max of two curves, or a piecewise rule; Range or domain of a rational function.

Functions for CAT: Formulas, Weightage & Question Types

Functions formula sheet

The 6 Functions question types CAT repeats

Is Functions costing you marks?

Functions in CAT: quick answers

More Algebra for CAT