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Invertible Functions Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Invertible Functions Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is an invertible function?
Ans. An invertible function, also known as a one-to-one function, is a function that maps each element of its domain to a unique element in its range. In other words, for every input, there is exactly one output, and vice versa.
2. How can you determine if a function is invertible?
Ans. To determine if a function is invertible, you can use the horizontal line test. If no horizontal line intersects the graph of the function more than once, then the function is invertible. Additionally, a function must also be one-to-one, meaning that it passes the vertical line test, where no vertical line intersects the graph more than once.
3. What is the inverse of an invertible function?
Ans. The inverse of an invertible function is a new function that undoes the actions of the original function. In other words, if the original function maps an input x to an output y, then the inverse function maps y back to x. The inverse function is denoted as f^(-1)(x).
4. Can all functions be inverted?
Ans. No, not all functions can be inverted. Only functions that are one-to-one, or injective, can be inverted. If a function is not one-to-one, then there would be multiple inputs that map to the same output, making it impossible to determine the original input from the output.
5. How can you find the inverse of an invertible function?
Ans. To find the inverse of an invertible function, you can follow these steps: 1. Replace the function's notation with y. 2. Swap the roles of x and y in the equation. 3. Solve the equation for y to express it in terms of x. 4. Replace y with f^(-1)(x) to denote the inverse function. 5. Verify that the inverse function is indeed the inverse by using composition, where applying the original function and its inverse to an input should yield the original input.
204 videos|288 docs|139 tests

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