# Algebra help needed for determining whether two functions are inverse of each other

Anonymous
timer Asked: Nov 1st, 2015
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### Question Description

For each pair of functions f and g below, find f(g(x)) and g(f(x)).  Then, determine whether f and g are inverse of each other.

Simplify answers as much possible.  Assume that your expressions are defined for all x in the domain of the composition.

A.  f(x)=x-3/2      B.  f(x)=6x

g(x)2x+3            g(x)=6x

f(g(x))=               f(g(x))=

g(f(x))=               g(f(x))=

f and g are inverses of each other                 A     B

f and g are not inverses of each other          A      B

## Tutor Answer

DrKarim
School: Purdue University

Thank you for the opportunity to help you with your question!

The Answers :

A. f(x)=x-3/2                                  B.  f(x)=6x

g(x)=2x+3                                        g(x)=6x

f(g(x))= (2x+3) -3/2                           f(g(x))=6(6x)

= 2x + 3/2                                        = 12x

g(f(x))=  2(x-3/2) + 3                            g(f(x))=6(6x)

= 2x - 3 + 3                                             = 12x

= 2x

f and g are not inverses of each other       A       B

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Anonymous
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