Given:


To find:
Whether f(x) and g(x) are inverse of each other by using that f(g(x)) = x and g(f(x)) = x.
Solution:
We know that, two function are inverse of each other if:
and 
We have,


Now,
![[\because g(x)=\dfrac{8}{x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20g%28x%29%3D%5Cdfrac%7B8%7D%7Bx%7D%5D)
![[\because f(x)=\dfrac{8}{x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20f%28x%29%3D%5Cdfrac%7B8%7D%7Bx%7D%5D)


Similarly,
![[\because f(x)=\dfrac{8}{x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20f%28x%29%3D%5Cdfrac%7B8%7D%7Bx%7D%5D)
![[\because g(x)=\dfrac{8}{x}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20g%28x%29%3D%5Cdfrac%7B8%7D%7Bx%7D%5D)


Since,
and
, therefore, f(x) and g(x) are inverse of each other.
Answer:

Step-by-step explanation:


Answer:
4 gallons
Step-by-step explanation:
80/5 will give you 16 so for each gallon the car can move 16 milles
so 64/16 = 4 so he will need 4 gallons of gas in order make the trip
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