Invertible Functions

Define Invertible Function.

Invertible functions are those function that has a unique inverse function, which can “reverse” the effect

What is the Condition for a Function to be Invertible?

For a function to be  invertible, functions needs to be a bijective (one-one and onto function).

How to Find the Inverse of a Function?

To find the inverse of a function switch the roles of dependent and independent variables and solve for original independent varible. The result of this process results in inverse of the function.

What is the Notation used for the Inverse of a function?

The inverse of a function f(x) is denoted as f^-1(x).

Can all Functions be Inverted?

No, all functions can’t be inverted only functions which are bijective i.e., one-one and onto, can be inverted.

What is the Domain of the Inverse of a Function?

Domain of the inverse of a function is the range of the original function.

How to Determine if a Function is One-One?

To determine function is one-one, take two arbitrary values in it’s domaine and equate value of function at those values. If those two aribitrary values cames out to be same, then function is one-one.

Are all Linear Functions Invertible?

No, all linear functions are not invertible as linear function with slope 0 i.e., graph parallel to x-axis are not invertible. Other than that, all linear functions are invertible.

As the name suggests Invertible means “inverse“, and Invertible function means the inverse of the function. Invertible functions, in the most general sense, are functions that “reverse” each other. For example, if f takes a to b, then the inverse, f^-1, must take b to a.