Answer:
200 miles will allow to stay within the budget
Step-by-step explanation:
∵ The daily budget is 82
∵ The cost per mile is 21/100 = $0.21
∵ The number of miles is x
∴ The equation of the budget is:
∴ 82 = 40 + 0.21 x
∴ 0.21 x = 82 - 40
∴ 0.21 x = 42
∴ x = 42/0.21 =200
∴ The number of miles = 200 to stay in the daily budget
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
Answer:
17x
Step-by-step explanation:
3x+4+4x+4+3x-4+3x-4+4x
Collect liketerms
Answer:
Denote adding term = a
a = (5/6x) - 4 - (1/2x) - 4
a = (5/6x) - (1/2x)
a = (5/6x) - (3/6x)
a = (2/6x)
a = (1/3x)
*******************************
a = (5/6)x - 4 - (1/2)x - 4
a = (5/6)x - (1/2)x
a = (5/6 - 1/2)x
a = (1/3)x
Hope this helps!
