Cheat sheet · JEE Preparation Mathematics

Relations and Functions (Class 11) cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

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JEE · Mathematics

Cheat sheet

Class 11 · Chapter 2Relations and Functions

A function sends every input to exactly one output.

1. Cartesian Product

A\times B = \{(a, b) : a\in A, b\in B\}

n(A\times B) = n(A)\,n(B)

Number of relations from A to B: $2^{mn}$ .

2. Relations & Functions

Relation: any subset of A × B; domain, codomain, range.
Function: every element of A has exactly one image.
Range ⊆ codomain.

3. Standard Functions

Function	Rule	Range
Identity	$f(x) = x$	$\mathbb{R}$
Constant	$f(x) = c$	$\{c\}$
Modulus	$f(x) = \|x\|$	$[0, \infty)$
Signum	$\dfrac{\|x\|}{x}$ , 0 at x = 0	$\{-1, 0, 1\}$
Greatest integer	$f(x) = [x]$	$\mathbb{Z}$
Reciprocal	$f(x) = \dfrac1x$	$\mathbb{R} - \{0\}$

4. Algebra of Functions

(f\pm g)(x) = f(x)\pm g(x)

\left(\dfrac fg\right)(x) = \dfrac{f(x)}{g(x)},\ g(x)\ne0

5. Key Points

Vertical line test for graphs of functions.
Polynomial functions have domain ℝ.
(a, b) = (c, d) ⇔ a = c and b = d.
A × ∅ = ∅.

Remember: A × B | function = one image | standard graphs

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