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
I think it's answer choice a
Answer:
All assets represent money, but only liquid assets can be easily turned into spendable money.
Step-by-step explanation:
Answer:
The sampling used is simple random sampling.
Step-by-step explanation:
Consider the provided information.
Types:
- Simple random sample is a subset of the population chosen from a larger set. Every person is selected by chance and randomly.
- Systematic sampling: list of elements is counted off.
- Convenience sampling: data which is readily available is used. That is, the first people are running into by the surveyor.
- Cluster sampling: divide the population into groups, usually geographically.
- Stratified sampling: divide population into groups called strata. but this time population might be separated into males and females.
Here, randomly selected 60 customers, Thus, the sampling used is simple random sampling.
Answer: 5(√3-1) unit.
Step-by-step explanation:
Since, By the below diagram,
For triangle BDC,
We can write,
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Now, In triangle ADC,
⇒ 
⇒ 
⇒ 
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⇒ 
