Inverse Functions IIT JEE Main Mathematics Online Mock Test Problem 61(April 15 2018 Evening)

TL;DR

Given a function f(x) = (x-1)/(x-2), find its inverse function by solving for x in terms of y.

Transcript

problem 61 let F be a function from A to B defined by f of X equals X minus 1 over X minus 2 here we're given the domain it's the set of real numbers except 2 and the codomain is the set of real numbers except 1 then f is and we have a couple choices so looks like we have to find the inverse of this function so f of X is equal to X minus 1 over X m... Read More

Key Insights

• ❣️ Finding the inverse function involves switching x and y and solving for x in terms of y.
• 🖐️ Domain and codomain restrictions play a crucial role in determining the validity of the inverse function.
• 🦻 Algebraic manipulation, including factoring and cancelling terms, aids in deriving the inverse function accurately.

Questions & Answers

Q: How do you find the inverse of a function?

To find the inverse of a function, switch x and y, solve for y, and then express x in terms of y to obtain the inverse function.

Q: Why are domain and codomain restrictions important in finding the inverse function?

Domain and codomain restrictions ensure that the inverse function is valid and unique, preventing any contradictions or inconsistencies in the function's behavior.

Q: What is the significance of the restrictions on y in the inverse function?

The restrictions on y in the inverse function ensure that the function remains well-defined and does not lead to division by zero or other mathematical inconsistencies.

Q: How does the algebraic manipulation lead to finding the inverse function?

By algebraically manipulating the function equation, we can derive the inverse function by expressing x in terms of y, leading to the inverse relationship between the two variables.

Summary & Key Takeaways

• The problem involves finding the inverse function of f(x) = (x-1)/(x-2) by switching x and y and solving for x in terms of y.

• After manipulating the equation, the inverse function is found as f^(-1)(y) = (2y-1)/(y-1).

• The domain and codomain restrictions must be considered to ensure the validity of the inverse function.