Question

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

Answer 1

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

Let's check out fog

fog = f(g(x))

$f(\frac{4x+1}{x})$

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

$\frac{1}{\frac{4x+1}{x}-4} =\frac{1}{\frac{4x+1-4x}{x}}=x$

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

$\frac{4(\frac{1}{x-4})+1}{\frac{1}{x-4}} = \frac{4+x-4}{1}=x$

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 .

Answer 2

Answer:

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

Step-by-step explanation: