Let f(x) be a function with domain [−3,∞) and range (−∞,2). If g(x)= f^−1(x) what is the domain of g(x+4)−7?
1 answer:
Answer:
- the domain of the function
is
- the range of the function
Step-by-step explanation:
If the function has the domain
and the range
then the function
has the domain that id the function's
range and the range that is function's
domain. Therefore,
- the domain of the function
is
- the range of the function
The function is the translation of the function
4 units to the left and 7 units down, hence
- the domain of the function
- the range of the function
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Answer:
And if we solve for a we got
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the hourly rates of a population, and for this case we know the distribution for X is given by:
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.20
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got