Question

For each pair of functions and below, find and .

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.)
f(x)=3/x,x=/= 0
g(x)=3/x, x=/=0
f(g(x))=
g(f(x))=
f and g are inverses of each other
f and g are not inverses of each other
f(x)=x+4
g(x)=-x+4
f(g(x))=
g(f(x))=
f and g are inverses of each other
f and g are not inverses of each other

Answer 1

1- Inverses .

2 - Not inverses.

Explanation:

Notice that

1 -

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

Since their composition is the identity, then they are inverses.

2 -

`f(g(x)) = ((-x+4)+4) = -x+8`

Since their composition is not the identity, then they are not inverses.