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Math / Discrete Mathematics and Its Applications 7 / Chapter 2 / Problem 10RQ

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

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a) Define the inverse of a function.________________b)

Chapter 2, Problem 10RQ

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QUESTION:

Problem 10RQ

a) Define the inverse of a function.

b) When docs a function have an inverse?

c) Does the function f(n) = 10 − n from the set of integers to the set of integers have an inverse? If so, what is it?

Questions & Answers

QUESTION:

Problem 10RQ

a) Define the inverse of a function.

b) When docs a function have an inverse?

c) Does the function f(n) = 10 − n from the set of integers to the set of integers have an inverse? If so, what is it?

ANSWER:

SOLUTION

Step 1

a)Definition of inverse of a function

Let A and B are any two non empty sets. Define a function $f:A\rightarrow{}B$ .

Then its inverse ${f}^{-1}:B\rightarrow{}A\$ is defined as ${f}^{-1}(\ f\ (\ x\ )\ )=x,\ \forall{}\ x\in{}A$

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