8, 17/12 9, 9/24 10, 13/10 11, 11/10
F(g(x)) = [(-7x-8)/(x-1) - 8} / [(-7x - 8)/(x-1) + 7] =
[(-7x - 8 - 8(x-1)) / (x-1)] / [(-7x - 8 + 7(x-1)) / (x-1)] = (-15x) / (-15) = x.
g(f(x)) = [-7*(x-8)/(x+7) - 8] / [(x-8)/(x+7) - 1] =
[(-7x + 56 -8*(x+7)) / (x+7)] / [(x - 8 - (x + 7)) / (x+7)] = (-15x) / (-15) = x.
So since f(g(x)) = g(f(x)) = x we can conclude that f and g are inverses.
6. Answer: B
Length of 1 side is 6
Perimeter is 6×6 = 36
5 times larger
Length of one side 6×5 = 30
Perimeter is the 30×6 = 180
180/36 = 5 Perimeter is 5 times greater
7. Answer: H
Find the whole number of squares in the shape given - 22 squares
22 × 10ft = 220 feet
8. Answer: F
((12-3)×3) + (4×3) = (9×3) + 12
= 27 + 12
= 39 ft^2
9. Answer: C
Answer:
the initial value -- f(0) -- results in a value of 1.5
Step-by-step explanation:
f(0) =
·
(any value raised to the power of zero equals one)
f(0) =
· 1
f(0) = 3/2 or 1.5
Answer:
C(t)=5000 -10t
Step-by-step explanation:
There are many examples in the real world of relationships that are functions.
For example, imagine a tank full of water with a capacity of 5000 liters, this tank has a small hole, by which 10 liters of water are lost every hour.
If we call C the amount of water in the tank as a function of time, then we can write the following equation for C:

Where:
C (t): Amount of water in the tank as a function of time
: Initial amount of water in the tank at time t = 0
a: amount of water lost per hour
t: time in hours
Then the equation is:
The graph of C (t) is a line of negative slope. This relation is a function since for each value of t there is a single value of C.
Its domain is the set of all positive real numbers t between [0,500]
Because the time count starts at t = 0 when the tank is full and ends at t = 500 when empty
Its Range is the set of all positive real numbers C between [0,5000] Because the amount of water in the tank can never be less than zero or greater than 5000Litres