Hello,Welcome to StudentBro.
Hello,Welcome to StudentBro.
Hello,Welcome to StudentBro.
Functions are one of the most important and high-weightage topics in JEE Mathematics. This chapter acts as a backbone for advanced topics such as Limits, Continuity, Differentiation, Integration, and Differential Equations. A strong understanding of functions helps students analyze mathematical relationships and interpret graphs effectively.
In JEE Main and JEE Advanced, questions from functions are often conceptual, graph-based, and application-oriented, making this chapter both scoring and challenging.
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♦ Set Theory and Relations ⇒ Download Here
♦ Function ⇒ Download Here
♦ Differentiation ⇒ Download Here
♦ Application of Derivatives ⇒ Download Here
♦ Indefinite Integral ⇒ Download Here
♦ Definite Integral ⇒ Download Here
♦ Area Under Curve ⇒ Download Here
♦ Differential Equations ⇒ Download Here
♦ Vector Algebra ⇒ Download Here
♦ 3D Dimensional ⇒ Download Here
♦ Determinants ⇒ Download Here
♦ Binary ⇒ Download Here
♦ Logarithm ⇒ Download Here
♦ Complex Number ⇒ Download Here
♦ Progression ⇒ Download Here
♦ Quadratic Equation ⇒ Download Here
♦ Permutations and Combinations ⇒ Download Here
♦ Binomial Theorem ⇒ Download Here
♦ Exponential ⇒ Download Here
♦ Rectangular Cartesian Co-ordinates ⇒ Download Here
♦ Straight Lines ⇒ Download Here
♦ Pair Of Straight Line ⇒ Download Here
♦ Circle System ⇒ Download Here
♦ Conic Sections ⇒ Download Here
♦ Trigonomerical Ratio ⇒ Download Here
♦ Trigonomerical Equation ⇒ Download Here
♦ Trigonomerical Properties ⇒ Download Here
♦ Height & Distances ⇒ Download Here
♦ Trigonomerical Inverse of Triangle ⇒ Download Here
♦ Hyperbolic Functions ⇒ Download Here
♦ Probability ⇒ Download Here
♦ Statistics ⇒ Download Here
♦ Statics ⇒ Download Here
♦ Dynamics ⇒ Download Here
♦ Numerical Method ⇒ Download Here
♦ Linear Programming ⇒ Download Here
♦ Maths Formula PDF for Entrance Exam ⇒ Download Here
A function is a special type of relation in which every element of the domain is associated with exactly one element of the codomain. Functions are usually represented as
f : A → B, where A is the domain and B is the codomain.
Understanding this definition clearly is essential, as many JEE questions test whether a given relation qualifies as a function.
Every function consists of three key components:
Domain – Set of all possible input values
Codomain – Set of all possible output values
Range – Set of actual output values
In JEE Maths, finding the domain and range of complex functions involving algebraic, trigonometric, logarithmic, or inverse expressions is extremely important.
JEE students must be familiar with various types of functions, including:
Constant Function
Identity Function
Polynomial Function
Rational Function
Modulus Function
Greatest Integer Function (GIF)
Exponential Function
Logarithmic Function
Trigonometric Functions
Each type has unique properties and graphs, which are frequently tested in exams.
Functions are classified based on symmetry:
Even Function – f(−x) = f(x), symmetric about the y-axis
Odd Function – f(−x) = −f(x), symmetric about the origin
JEE problems often test these properties using graphs or algebraic expressions.
A function is periodic if f(x + T) = f(x), where T is the period.
Trigonometric functions like sin x, cos x, and tan x are common examples.
Understanding periodicity is crucial for solving JEE questions involving transformations and multiple solutions.
Graphical interpretation plays a major role in JEE Maths. Students should be able to:
Sketch standard graphs
Identify transformations like shifting, reflection, and scaling
Analyze increasing and decreasing nature
Understand maxima and minima visually
Many JEE questions are solved faster using graph-based approaches rather than lengthy calculations.
If f and g are two functions, then the composite function is defined as
(f ∘ g)(x) = f(g(x))
JEE problems often test:
Domain of composite functions
Simplification of expressions
Graph interpretation of composite functions
Conceptual clarity is key to avoiding mistakes in this section.
A function is invertible if it is one-one (injective) and onto (surjective).
One-One Function – Different inputs give different outputs
Onto Function – Every element of codomain has a pre-image
Inverse functions are widely used in logarithmic, trigonometric, and calculus-based JEE problems.
The inverse of a function f is denoted by f⁻¹, such that
f(f⁻¹(x)) = x
Finding inverse functions requires careful consideration of domain restrictions, which is a common JEE exam trap.
Many-One Function – Multiple inputs have the same output
Into Function – Range is a proper subset of the codomain
JEE often asks students to identify these properties from given graphs or equations.
Some important properties tested in JEE include:
Monotonicity
Boundedness
Symmetry
Continuity (basic understanding)
These properties help in solving higher-level questions in calculus.
Students often struggle due to:
Incorrect domain selection
Ignoring function definition conditions
Errors in graph interpretation
Confusion between inverse and reciprocal
Avoiding these mistakes can significantly boost JEE scores.
Functions are essential because they:
Form the base of calculus
Appear in almost every JEE Maths paper
Improve analytical and graphical skills
Help connect multiple chapters
A strong command over functions ensures smoother preparation for advanced topics.
Practice domain and range problems daily
Memorize standard graphs
Solve previous year JEE questions
Focus on conceptual understanding
Using structured study material from StudentBro can help students master this chapter efficiently.
Functions are a core pillar of JEE Mathematics. With strong conceptual clarity, regular practice, and proper graph analysis, students can turn this chapter into a high-scoring area. StudentBro provides well-organized, exam-oriented content to help students excel confidently in JEE Main and Advanced.
