141k views
1 vote
For each pair of functions f, g below, find f(g(x)) and g(f(x))

Then, determine whether and are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all in the domain of the composition.
You do not have to indicate the domain.)

For each pair of functions f, g below, find f(g(x)) and g(f(x)) Then, determine whether-example-1

1 Answer

4 votes

Answer:

See below

Explanation:

Part A


f(g(x))=f((x)/(3))=3((x)/(3))=x\\g(f(x))=g(3x)=(3x)/(3)=x

Since BOTH
f(g(x))=x and
g(f(x))=x, then
f and
g are inverses of each other

Part B


f(g(x))=f((x+1)/(2))=2((x+1)/(2))+1=x+1+1=x+2\\g(f(x))=g(2x+1)=((2x+1)+1)/(2)=(2x+2)/(2)=x+1

Since BOTH
f(g(x))\\eq x and
g(f(x))\\eq x, then
f and
g are NOT inverses of each other

User Themacco
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.