Question 1200539
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<font color=red>Answers:</font>
<ol type="a"><li>{{{-7<= y <=2}}} which has the interval notation [-7, 2]</li><li>{{{-7<= x <=2}}} which has the interval notation [-7, 2]</li></ol>Explanation:


f(x) is defined only when 0 ≤ x ≤ 3


Refer to the 2nd graph the tutor Edwin McCravy had made.
That graph shows (3,-7) is the lowest point on the parabola. 


When completing the square, 
f(x) = x^2-6x+2
becomes
f(x) = (x-3)^2-7
Use the FOIL rule to confirm this is the correct vertex form.


The highest point is (0,2)
We can determine this by plugging x = 0 to get y = 2.


The range is the set of possible y outputs.
y = -7 is the smallest output
y = 2 is the largest output
Therefore, {{{-7<= y <=2}}} represents the range.
y is between -7 and 2 including both endpoints.
In interval notation, this is [-7, 2]
The square brackets tell the reader to include the endpoints.


Recall the process of finding the inverse means we swap x and y, then solve for y.
Because of this swap, the domain and range swap when going from the original function to the inverse.


Therefore,
*[tex \Large \text{range of original} \leftrightarrow \text{domain of inverse}]
which means
original has range {{{-7<= y <=2}}} leads to the inverse having the domain {{{-7<= x <=2}}}. All we do is swap y for x.
You can use the last graph Edwin McCravy had made as visual confirmation. 


<a href="https://www.geogebra.org/calculator">GeoGebra</a> and <a href="https://www.desmos.com/calculator">Desmos</a> are two of many graphing tools you can use to verify the answer.
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