Are the functions inverse of each other? f(x)=5x^2+3, g(x)sqrt x-3/5
2 answers:
Answer:
no
Step-by-step explanation:
The function f(x) does not pass the horizontal line test, so has no inverse, except on a restricted domain. The question does not include any restriction on the domain, so the functions are not inverses of each other.
If we assume your functions are ...
Then the value of g(f(x)) is ...
This is only equal to x when x ≥ 0. For x < 0, g(f(x)) ≠ x, so the functions are not inverses.
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You can see from the graph that the function g(x) is not the reflection of f(x) across the line y=x. If the functions were inverses, each would be a reflection of the other.
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Answer:
Step-by-step explanation:
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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
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".
Data given
n = 25000 represent the automobile policy holders
represent the population mean
represent the population standard deviation
Let T the variable that represent the total of interest on this case. We can assume that the random variable for an individual policy holder is given by:
From the central limit theorem we know that the distribution for the sample mean is given by:
Solution to the problem
First we need to find the distribution for the random variable T like this:
And the total T is given by:
We can find the expected value, variance and deviation for this random variable like this:
And we are interested on this probability:
And we can use the Z score formula given by: