X=12/11 for the first one
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:
D
Step-by-step explanation:
So if Arturo's family hires 3 painters for $50 an hour each, how much do they spend?
X= Charge for number of number of hours
Now let's say that each of the painters worked only <u>one </u> hour each.
That would be take a long time to add up so you multiply.
$50 x 3
In other words it's $50 + $50 + $50.
$50 x 3 = $150
Now X stands for the amount of money paid to each artist. In this case, X= $50. So we already figured out X. X is $50. It is a mistake to add the X at the end of the answer because X is already there in a numerical form. So the answer is D, $150.
Answer:
D
Step-by-step explanation:
it was right on edge
Answer:
$22350 is the predicted value of portfolio.
Step-by-step explanation:
The given expression is 1.08s + 1.02b1.08s + 1.02b which predicts the end of year value of a financial portfolio.Here s = value of stocks and b = value of bonds.
Now we have to calculate the value of a portfolio with s = $200 and b = $100
So we will put the values of s and b in the given expression to calculate the value portfolio.
1.08×200 +1.02×(100)×1.08×(200)+ 1.02×(100) = 216 + 22032 + 102
= $22350
The predicted end to end year value of portfolio is = $22350
