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Important Formulas: Relations & Functions | Mathematics (Maths) for JEE Main & Advanced PDF Download

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FAQs on Important Formulas: Relations & Functions - Mathematics (Maths) for JEE Main & Advanced

1. What are the key functions that JEE aspirants need to know for the exam?
Ans. JEE aspirants should focus on several key functions including polynomial functions, exponential functions, logarithmic functions, trigonometric functions, and their inverses. Understanding their properties, graphs, and how to solve equations involving these functions is crucial for success in the exam.
2. How can I graph a polynomial function effectively for JEE?
Ans. To graph a polynomial function effectively, first identify the degree and leading coefficient to determine the end behavior. Next, find the x-intercepts by setting the function to zero and solving for x. Additionally, identify any critical points and inflection points by taking the derivative, which helps in sketching the curve accurately.
3. What are the common properties of exponential functions that JEE students should memorize?
Ans. Common properties of exponential functions include that they always pass through the point (0, 1), never touch the x-axis (asymptotic behavior), and their growth rate increases rapidly as the input increases. Additionally, the base of the exponential function affects its growth; for instance, a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.
4. How do I solve logarithmic equations for the JEE exam?
Ans. To solve logarithmic equations, first apply the properties of logarithms to simplify the equation. This might involve using the change of base formula or combining logarithms with the same base. After simplification, convert the logarithmic form to the exponential form, and then solve for the variable. Always check for extraneous solutions due to the nature of logarithms.
5. Why is it important to understand the domain and range of functions for JEE?
Ans. Understanding the domain and range of functions is crucial for JEE as it helps in identifying valid input values and corresponding output values for functions. This knowledge is essential for solving problems correctly, especially in calculus and higher-level mathematics where limits and continuity are involved. It also aids in graphing functions accurately.
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