Question
Asked Jan 26, 2020
2 views

Let S = {1, 2, 3}. Determine whether the functions f : S → S defined as
below have inverses. Find f-1, if it exists.
(a) f = {(1, 1), (2, 2), (3, 3)}
(b) f = {(1, 2), (2, 1), (3, 1)}
(c) f = {(1, 3), (3, 2), (2, 1)}

check_circle

Expert Answer

Step 1

A function has an inverse iff f is one-one onto.

If inverse of f exists then we have

Algebra homework question answer, step 1, image 1
fullscreen
Step 2

(a) Here f is one-one onto , so inverse of f exist 

Algebra homework question answer, step 2, image 1
fullscreen
Step 3

(b) Here f is not one-one as f(2)=f(3)=1 .Also f is not onto because there ...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Algebra

Other