Step-by-step explanation:
85 is the answer you are looking for
F(x)=
![\sqrt[3]{x+2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%2B2%7D%20)
to solve for the inverse of a function you do 4 steps:
1. subsitute f(x) with y
2. switch y and x places
3. solve for y
4. subsitute y with f⁻¹(x)
so we have
f(x)=
![\sqrt[3]{x+2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%2B2%7D%20)
subsitute f(x) with y
y=
![\sqrt[3]{x+2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7Bx%2B2%7D%20)
switch x and y
x=
![\sqrt[3]{y+2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7By%2B2%7D%20)
solve for y
x=
![\sqrt[3]{y+2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7By%2B2%7D%20)
cube both sides
![x^{3}](https://tex.z-dn.net/?f=%20x%5E%7B3%7D%20)
=y+2
subtract 2 from both sides
![x^{3}-2](https://tex.z-dn.net/?f=%20x%5E%7B3%7D-2%20)
=y
subsitute y with f⁻¹(x)
f⁻¹(x)=
![x^{3}-2](https://tex.z-dn.net/?f=%20x%5E%7B3%7D-2%20)
the answer is f⁻¹(x)=
Answer:
a) 91 1/6 gallons
b) 2502 miles
Step-by-step explanation:
You are given a number of miles and a number of gallons for the car. The ratio of these numbers is ...
(261 mi)/(14.5 gal) = 18 mi/gal
We presume this value is constant for this car. Then the questions can be answered by forming and solving a proportion:
a) 1641 miles/(gallons) = 18 mi/(1 gal)
Multiplying by gallons and dividing by 18 mi/gal, we get
1641/18 gal = (gallons) = 91 1/6 gal
It will take 91 1/6 gallons of gasoline for Mary to drive to her friend's house.
___
b) Same deal, but the miles are unknown.
(miles)/(139 gal) = (18 mi)/(1 gal)
Multiplying by 139 gal gives ...
(18 mi)·139 = (miles) = 2502 mi
139 gallons of gasoline will let Mary drive 2502 miles.
Answer is A and B. Solutions are where the two graphs cross, so you just need to find those coordinates, which are (-5,-13) and (2,-6).