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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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In 44-55 indicate which of the functions in the referenced exercise are one-to-one correspondences. For each function that is a one-to-one correspondence, find the inverse function.

Exercise 18 with the co-domain taken to be the set of all real numbers not equal to 1

To determine

To check:

Whether the given function is one-to-one correspondence and also find the inverse of the given function if it exists.

Explanation

Given information:

f(x)=x+1x1 for all real numbers x1.

Concept used:

One-to-one function: The distinct elements in domain are mapped with distinct elements in co-domain.

Onto function: Every element in co-domain must be mapped with the element in domain.

Calculation:

Given that f:R{1}R{1},f(x)=x+1x1

To show f is one-to-one correspondence, we need to show that f is one-to-one and onto.

To show f is one-to-one,

Let          f(x1)=f(x2)x1+1x11=x2+1x21(x21)(x1+1)=(x11)(x2+1)x2x1=x1x22x2=2x1x2=x1

Hence, f is one-to-one

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