I'm doing a practice, and I'm really confused by this question. Help would really be appreciated!!! **100 PTS!**
2 answers:
Great Question!
The problem we have at hand is known to be a function, which maps elements from one set of objects, ( the domain ) onto another, the range. If we were to consider an ordered pair, say ( x, y ), then the function would map x onto y. The inverse function is simply the reverse. Take the ordered pair (-4,0). Function g would map - 4 onto 0, such that . Therefore, the inverse function would map 0 onto - 4, resulting in
. And there you have it! Our first part is answered!
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This second bit here is interesting. Let -
- Switch x and y,
- And now solve this equation for y,
As you can see, we have taken the inverse of h( x ). As y = h( x ), we can thus conclude the following -
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The composition (h^-1 o h)(-5) is, in other words, h^-1(h(-5)). We can therefore calculate h(-5) and then take it's inverse -
Now we can take it's inverse -
Our solution for this last bit is - 5. And, if you don't feel like reading through this entire explanation just take a look at the " summed up " answer below,
I do hope that helps you!
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Answer: No , at 0.05 level of significance , we have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.
Step-by-step explanation:
Let denotes the average hours of sleep per night.
As per given , we have
, since is left-tailed and population standard deviation is unknown, so the test is a left-tailed t -test.
Also , it is given that ,
Sample size : n= 22
Sample mean :
Sample standard deviation : s= 1.93
Test statistic :
i.e.
For significance level and degree of freedom 21 (df=n-1),
Critical t-value for left-tailed test=
Decision : Since the test statistic value (0.58) > critical value 1.7207, it means we are failed to reject the null hypothesis .
[Note : When , then we accept the null hypothesis.]
Conclusion: We have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.