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.

Question

contestada

Respuesta :

ACCESS MORE ACCESS MORE ACCESS MORE ACCESS MORE

Riia Riia · Answer 1 · 2018-07-30T18:00:53+02:00

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

Let's check out fog

fog = f(g(x))

[tex] f(\frac{4x+1}{x}) [/tex]

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

[tex] \frac{1}{\frac{4x+1}{x}-4} =\frac{1}{\frac{4x+1-4x}{x}}=x [/tex]

Domain

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

[tex] (-\infty,0)U(0, \infty) [/tex]

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

[tex] \frac{4(\frac{1}{x-4})+1}{\frac{1}{x-4}} = \frac{4+x-4}{1}=x [/tex]

Domain

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

SO domain is

[tex] (- \infty,4)U(4, \infty) [/tex]

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

aidanskiles18 aidanskiles18 · Answer 2 · 2020-09-24T04:38:19+02:00

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:

Answer Link