    # Inverse Of A Function If f: A -> B is a one-one onto (or bijective) function and if f(x) = y, where x A, y B then f1 : B -> A defined by f1 (y) = x, is known as inverse function of f.

A function whose inverse exists (i.e. if it is bijective) is called an Invertible function.

For example:
• If A = {2, 4, 6} and B = {5, 7, 9} and f: A -> B is given by f(2) = 5, f(4) = 7 and f(6) = 9.
Find f 1.

Solution:

Given that f(2) = 5, f(4) = 7 and f(6) = 9,

Hence f = {(2,5), (4, 7), (6, 9)}

Hence f1 = {(5, 2), (7, 4), (9, 6)}

• Let f: N -> R defined as f(x) = x2 + 4x + 8, then show that f: N -> A, where A is the range of f, is invertible. Also find f1.

Solution: f(x1) = f(x2) => x12 + 4 x1 + 8 = x22 + 4 x2 + 8

=> (x12 � x22) + 4(x1 � x2) = 0

=> x1 = x2

Hence f is one-one.

Let y A be any element then f(x) = y

=> x2 + 4x + 8 = y

=> y = (x + 2)2 + 4

=> x = (√y - 4 � 2), x R

And f(√y - 4 � 2) = (√y - 4 � 2)2 + 4(√y - 4 � 2) + 8 = y => f is invertible.

Hence f1: A -> N can be defined as f1(x) = (√x - 4 � 2).

Online Inverse of a Function (Invertible) Help:

If you are stuck with a Inverse of a Function (Invertible) Homework problem and need help, we have excellent tutors who can provide you with Homework Help. Our tutors who provide Inverse of a Function (Invertible) help are highly qualified. Our tutors have many years of industry experience and have had years of experience providing Inverse of a Function (Invertible) Homework Help. Please do send us the Inverse of a Function (Invertible) problems on which you need Help and we will forward then to our tutors for review.

Online Tutor Inverse of a Function (Invertible):

We have the best tutors in math in the industry. Our tutors can break down a complex Inverse of a Function (Invertible) problem into its sub parts and explain to you in detail how each step is performed. This approach of breaking down a problem has been appreciated by majority of our students for learning Inverse of a Function (Invertible) concepts. You will get one-to-one personalized attention through our online tutoring which will make learning fun and easy. Our tutors are highly qualified and hold advanced degrees. Please do send us a request for Inverse of a Function (Invertible) tutoring and experience the quality yourself.       • 