Question

A. Use the composition to prove whether or not the functions are inverses of each other.

B. Express the domain of the compositions using interval notation.

Answer 1

so basically you do the answer over and over till you get it right cuz thats what my momma told me to do and mommas always right

Explanation:

Answer 2

Here we need to find fog and gof, and they must be equal to x .

Let's check out fog

fog = f(g(x))

`f((4x+1)/(x))`

Substituting the value of g(x) in f(x) for x, we will get

`(1)/((4x+1)/(x)-4) =(1)/((4x+1-4x)/(x))=x`

Domain

Here the input function is g(x), and the denominator should not be 0. So x should not be zero. Therefore, domain is

`(-\infty,0)U(0, \infty)`

Now let's check gof

gof = g(f(x))

Here we need to insert f(x) in g(x) for x, and on doing that , we will get

`(4((1)/(x-4))+1)/((1)/(x-4)) = (4+x-4)/(1)=x`

Domain

Here the input function is f(x), and denominator should not be zero.

SO domain is

`(- \infty,4)U(4, \infty)`

Since fog = gof =x, so the given function are inverses of each other .