F(x)=1/x-5, g(x)=5x-1/x 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.

Not inverse of each other

Domain : [-∞,0) U (0,5) U (5,∞]

Step-by-step explanation:

Given in the question two functions

f(x)=1/x-5

g(x)=5x-1/x

To find that each of them are inverse of each other we will use composition

take LCM

5x will be cancel

1 ÷ (-1/x)

1 × (-x/1)

-x

Now,

×

10-x

As it ended up with different answers, so f(x) and g(x) are not inverse of each other

The domain are all the possible x-values of function except x ≠ 0 and x ≠ 5

We can conclude that the domain of the composition function is

Domain : [-∞,0) U (0,5) U (5,∞]

answer: idk

step-by-step explanation: