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2 answers:
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that is correct hmmmm, yes, I think the restriction is also correct, it has to be x > 0, because, the domain on the original, has a restriction of x⩾3, otherwise the radicand turns negative.
now, the graph of that original function is a parabola sideways opening to the right, if you include both sides of the vertex of the parabola, it will not pass the vertical-line-test and not be a function, but if you restrict it to only positive roots, so it'll only be on the 1st quadrant, then it functions ok.
that means, the range of the original function, has to stick to only 0 or positive root values, now, recall that the range of the original is the domain of the inverse. Therefore, the domain of the inverse, will have to stick to only 0 or positive values, since it's bound to the same restriction as the original's range.
notice the picture below of both, the dashed section is the positive range for each, if you include it, the original will fail the vertical-line-test, and the inverse will fail the horizontal-line-test.
recall that for a function to have an inverse, they both must pass the vertical and horizontal line test, or be a one-to-one functions.
Answer:
99.38%
Step-by-step explanation:
We have that the mean (m) is equal to 124, the standard deviation (sd) 6.4 and the sample size (n) = 64
They ask us for P (x <126)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / (sd / (n ^ 1/2))
We have all these values, replacing we have:
z = (126 - 124) / (6.4 / (64 ^ 1/2))
z = 2.5
With the normal distribution table (attached), we have that at that value, the probability is:
P (z <2.5) = 0.9938
The probability is 99.38%
