Step-by-step explanation:
1/ 3 is the probability of getting one head
We have the function:
f(x) = 3x / (x + 7)
(a)
We rename the function as: f(x) = y
Then:
y = 3x / (x + 7)
Taking the inverse:
1/y = (x + 7) / 3x
1/y = x/3x + 7/3x
1/y = 1/3 + 7/3x
Solving for x:
1/y - 1/3 = 7/3x
1/x = 3/7y - 1/7 = (3 - y) / 7y
Taking the inverse:
x = 7y / (3 - y)
Then, the inverse function of f is:
f ⁻¹(x) = 7x / (3 - x)
(b)
We know that the division by 0 is undefined in real numbers. From the function f, we have a division by 0 if x = -7, so the domain should be:
Dom_f = {x| x ≠ -7}
For the range, we know that x = -7 is a vertical asymptote of the function f, so this means that the graph never passes across x = -7, but it tends to it on infinity. Then, the range of f is:
Ran_f = All the real numbers
For f ⁻¹(x), we see that for x = 3 there is a division by 0, so this is an asymptote of the function. Then, the domain of f ⁻¹ is:
Dom_f ⁻¹ = {x| x ≠ 3}
Again, as there is an asymptote, the range is:
Ran_f ⁻¹ = All the real numbers
(3,452 * 2) = round trip = 6,904.
6,904 * 3 = total distance = 20,712.
Therefore, the final answer is 20,712 miles.
Answer: The correct option is 1, i.e., 
.
Explanation:
The geometric sequence is in the form of,
Where, a is the first term of the sequence and r is the common ratio of the sequence.
It means the 
term of the sequence is defined as,
So the the 
term of the sequence is defined as,
It means the geometric sequence is in the form of,
Where, r be any constant.
From the options only is in the form of with common ratio 
.
Therefore, the function can be used to model the graphed geometric sequence is .
Convert the mixed number to an improper fraction:
Subtract the fractions to get your final answer:
