Simplifying and Solving
3√(6x-6) = 6
x = 37
Find the inverse of the following equation:
f(x) = 2,317x2 - 417
f-1(x) = √((x+417)/(2317))
Find the inverse of the following equation:
f(x) = -3 3√(y)
f-1(x) = (x/-3)3
Use the composition of functions to determine of g(x) is the inverse of f(x).
f(x) = 2x2-14
g(x) = -2√(x) + 14
If g(x) is not the inverse of f(x), find f-1(x).
They are not inverses.
f-1(x) = √((x+14)/(2))
1/3√(x+8) + 8 = 10
x = 28
Find the inverse of the following equation.
f(x) = 2√(x) - 6
f-1(x) = ((x+6)/(2))2
Find the inverse of f(x) algebraically.
f(x)=(x-2)3 + 7
f-1(x) = 3√(x-7) + 2
After using the composition of functions, you find that both (f o g)(x) and (g o f)(x) equal x.
Are f(x) and g(x) inverses? Why or why not?
Yes, f(x) and g(x) are inverses.
Since both (f o g)(x) and (g o f)(x) equal x, and x = x, we can determine that they inverses.
√(4x-10) = √(x-19)
x = -3
Cody's grade on an Algebra II test is entirely dependent on how many hours of studying he puts in, as shown in the following equation, where S represents hours studied and G represents his grade:
20S2 = G
If he got a 96.8 on the test, determine how many hours he spent studying by finding the inverse of the equation.
S = √(G/20)
Cody spent 2.2 hours studying for the test.
John Smith found the inverse of f(x) = 3√(12x) - 2 to be f-1(x) = ((x+2)3/(12)). Is he correct?
Yes, the inverse of f(x) = 3√(12x) - 2 is f-1(x) = ((x+2)3/(12)).
In his math class, Billy-Bob found the inverse of the equation below to be f-1(x) = (-2x)3 + 2.
f(x) = -½ 3√(x + 2)
Use the composition of functions to determine if he is right. If he isn’t, solve for the correct inverse of the problem.
Billy-Bob is not right, as (f ○ f-1)(x) = -½ 3√(-2x3 + 4); the correct inverse of this problem is f-1(x) = (-2x)3 ‒ 2.
3√(x+17) - 9 = 7
x = 4079
To determine the height of a building, architects Billy-Bob Bobertson and Frankie-Fro Fransiscan used the following equation which derives the height, H, from the area, A:
H = ½√A ‒ 10
They measure the height of the building to be 13.84 feet. Find the area.
Find the inverse of the equation to make it solve for height (A = (2H + 10)2). The area of the building is approximately 2274.72 square feet.
The amount of times Allison hits a curb on her way to work in one given day is entirely dependent on how many thermoses of coffee she drinks in the morning, as shown in the following equation, where T represents how many thermoses of coffee she drinks and C represents how many curbs she hits:
3√(T) -1 = C
If she hits 3 curbs on her way to work, determine how many thermoses of coffee she drank by finding the inverse of the equation.
T = (C - 1)3
Allison drank 8 thermoses of coffee.
Determine the functions are inverse of each other using composition of functions
f(x) = x2 + 5
g(x)= 2√(x-5)
They are inverses; both equal x.
√(80x - 16) = 3x + 2
x = {.3066, 7.25}
The height of John can be solved with the following equation:
3√(W) + 3 = H
If John is 68.45 inches tall, determine his weight by finding the inverse of the equation.
John weighs about 476 pounds.
The amount Carlos can bench press in a given day is somehow directly correlated to how much he sleeps the night before, as shown in the following equation, where S represents hours slept and B equals how much he can bench press in pounds:
S3 + 64 = B
If Carlos bench presses 67.375 pounds, find the inverse of the equation and determine how long he slept.
S = 3√(B-64)
Carlos slept for 1.5 hours.
Determine the functions are inverse of each other using composition of functions
f(x) = √(2x) + 1
g(x)= 2x2-1, x>=0
They are not inverse functions.