Home
Learn
Plan & Focus
Community
Pricing
Play & Compete
Free Resources

Log in Join Free

by JEE Master

Ask. Share. Learn. Grow Together. India's all-in-one community for JEE Main & JEE Advanced aspirants.

Explore

Learn
Plan & Focus
Community
Play & Compete
Free Resources

Resources

JEE Main PYQs
JEE Advanced PYQs
Formula Sheets
NCERT Mapping
Mock Analysis

Support

Help Center
Privacy Policy
Terms of Use
Contact Us

© 2026 PadhoNa. All rights reserved.

Formula Sheets / Maths

Chapter 14

Functions

Revise with flashcards Download this chapter (PDF) All Maths formulas (PDF)

Types of functions Special functions Even, odd and periodic Composite and inverse

Types of functions

Counting
$∣ A ∣ = m, ∣ B ∣ = n : n^{m}$ functions $;$ $^{n} P_{m}$ one-one $(n \geq m)$
Onto functions
$k = 0 \sum n (- 1)^{k}^{n} C_{k} (n - k)^{m}$ onto maps from $m$ to $n$ elements
Bijection
one-one and onto $;$ $[x + n] = [x] + n (n \in Z),$ bijections when $∣ A ∣ = ∣ B ∣ = n$

Special functions

Greatest integer
$[x] \leq x < [x] + 1,$ $[x + n] = [x] + n (n \in Z),$ $[x] + [- x] = {0, - 1, x \in Z x \in / Z$
Fractional part
${x} = x - [x] \in [0, 1)$
Signum
$sgn x = \frac{∣ x ∣}{x} (x \neq = 0),$ $sgn 0 = 0$

Even, odd and periodic

$f (- x) = f (x)$ even $;$ $f (- x) = - f (x)$ odd $;$ $f (x) = even \frac{f ( x ) + f ( - x )}{2} + odd \frac{f ( x ) - f ( - x )}{2}$
Periods
$sin x, cos x : 2 π;$ $tan x : π;$ $∣ sin x ∣ : π;$ ${x} : 1;$ $f (a x + b) : \frac{T}{∣ a ∣}$

Composite and inverse

$(f \circ g) (x) = f (g (x)),$ $(f \circ g)^{- 1} = g^{- 1} \circ f^{- 1},$ $f (f^{- 1} (x)) = x$
$f^{- 1}$ exists only if $f$ is a bijection; its graph is the mirror image of $f$ in $y = x$ .

Sets and Relations Limits