Let f ( x ) = ( x + 3 ) ^2
1 answer:
Answer:
f(x) restricted to x in [-3, ∞) will have inverse function f⁻¹(x) = √x -3
Step-by-step explanation:
The given function is non-decreasing on the interval [-3, ∞), so that is a suitable domain.
The inverse function can be found from ...
x = f(y) = (y +3)^2
√x = y +3
√x -3 = y
So, the inverse function of f(x) on the domain [-3, ∞) is ...
f⁻¹(x) = √x -3
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In the attached graph, the solid red curve is the domain-restricted portion of f(x). The blue curve is the inverse function. The dashed orange line is a reference line to help you see that the inverse function is a reflection of the function across that line.
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Answer:
a)
b)
If we compare the p value and the significance level given we see that we have enough evidence to reject the null hypothesis at 5% of significance.
Step-by-step explanation:
Data given and notation
n=114 represent the random sample taken
estimated proportion of people that their approval rating might have changed
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Hypothesis
We need to conduct a hypothesis in order to test the claim that true proportion of people that their approval rating might have changed is 0.58 or no.:
Null hypothesis:
Alternative hypothesis:
Part a
(1)
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Part b: Statistical decision
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
If we compare the p value and the significance level given we see that we have enough evidence to reject the null hypothesis at 5% of significance.