A. use composition to prove whether or not the functions are inverses of each other.
b. express the domain of the compositions using interval notation.

Hello mate!

A composition of two functions is when a function is valuated in the other:

this is for f(x) and g(x); f(g(x))

now a the functions are inverse if: f(g(x)) = x  

in this case and

then

now let's simplify it:

Now let's see g(f(x)), we can suppose that this is also equal to x, but let's prove it:

as we expected, then f(x) and g(x) are inverses of each other.

b) the composition f(g(x)) = x

is true that the domain of f(x) is the set of all real numbers different to 3, and the domain of g(x) is the set of all real numbers except the 0 ( you can see the exceptions by loking when the denominator is equal to 0)

but in the composition there are not a problem with the denominator (the denominator is equal to 1 in this case)

so the domain of the composition is the set of all real numbers

x

step-by-step explanation:

c: lkllmn.

hope it's you