Mathematics, 15.10.2020 06:01 eviepack

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Answer from: Gaby702

$f^{-1}(x)=\sqrt{x+1}-3$

Step-by-step explanation:

We have the function:

f(x)=y=x^2+6x+8 with the domain restriction $\{x\geq -3\}$ .

And we want to find the inverse of our function.

To find the inverse of our function, we take the following steps:

1) Swap x and y. 2) Solve for y.

Therefore, our inverse will be:

x=y^2+6y+8

First, let's subtract 8 from both sides. So:

x-8=y^2+6y

To solve for y, we can complete the square. To complete the square, we:

1) Divide the coefficient of the b term by 2. 2) Square that. 3) Add that number to both sides.

Our b term is 6. 6/2=3 , and 3^2=9 . So, we will add 9 to both sides. This yields:

(x-8)+9=(y^2+6y+9)

Simplify the left. Complete the square on the right. So:

x+1=(y+3)^2

Take the square root of both sides and solve for y:

$y+3=\sqrt{x+1}\Rightarrow y=\sqrt{x+1}-3$

Subtract 3 from both sides. So, our inverse is:

$f^{-1}(x)=\sqrt{x+1}-3$

Part 2)

See below for graph.

Here is also a good time to reinforce the idea of inverses. Notice that the domain of our original function f(x) is $x\geq-3$ . So, this means that the range of f(x) is (looking at the graph) is $y\geq-1$ .

When we find the inverse, we will flip the domain and range. Therefore, the domain of our inverse function will be the range of our original function, and the range of our inverse function will be the domain of our original function.

From the graph, we can see that f⁻¹(x) has a domain of $x\geq-1$ and a range of $y\geq -3$ . Therefore, their domain and range are indeed opposites.

And we're done!

Answer from: Quest

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation:

Answer from: Quest

A) for the n row: 22+(n-1)×6therefore,b) 100-22=78that means (n-1)×6=7878÷6=1313+1=1414th row has 100 seats

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