Since f(x) is (strictly) increasing, we know that it is one-to-one and has an inverse f^(-1)(x). Then we can apply the inverse function theorem. Suppose f(a) = b and a = f^(-1)(b). By definition of inverse function, we have
f^(-1)(f(x)) = x
Differentiating with the chain rule gives
(f^(-1))'(f(x)) f'(x) = 1
so that
(f^(-1))'(f(x)) = 1/f'(x)
Let x = a; then
(f^(-1))'(f(a)) = 1/f'(a)
(f^(-1))'(b) = 1/f'(a)
In particular, we take a = 2 and b = 7; then
(f^(-1))'(7) = 1/f'(2) = 1/5
Answer:
- 23/13
Step-by-step explanation:
1. Subtract 5/2 from both sides of the equation.
2. Simplify
7/5 = /10 − 23/10
3. Multiply all terms by the same value to eliminate fraction denominators.
7/5 = /10 − 23/10 2 ⋅ 5 ⋅ 7/5 = 2 ⋅ 5( /10 − 23/10)
4. Simplify
14 = − 23
5. Subtract from both sides of the equation.
14 = − 23 14 − = − 23 −
6. Simplify
13 = − 23
7. Divide both sides of the equation by the same term.
13<em>x </em>= −23 13x/13 = -23/13
8. Simplify
= −23/13
Answer:
number of gallons of water the family will use every morning = 50 gallons
Step-by-step explanation:
Every minutes 2.5 gallons of water flows from the shower . The amount of water disperse by the shower for every 1 minutes is 2.5 gallons. The family using the shower are 4 in numbers . And each of them spend on average of 5 minutes showering .
Let us find how many gallons of water will flow for 5 minutes since family member spent an average of 5 minutes bathing every morning/. Therefore,
2.5 gallons = 1 minutes
? gallons = 5 minutes
cross multiply
number of gallons of water each family member uses every morning = 2.5 × 5 = 12.5 gallons
They are 4 family members in number since each person uses 12.5 gallons of water , 4 of them will use 4 × 12.5 = 50 gallons
Answer:
This is a rectangular prism
Step-by-step explanation:
As you can see from my attachment, this figure models a rectangular prism when put together :)
Answer:
An object that weighs 100 tons and is floating is displacing exactly 100 tons of the fluid, and the buoyant force on it is 100 tons. The vertical forces on it are balanced (add up to zero), and that's why it isn't accelerating up or down.
Step-by-step explanation:
Correct me if im wrong