Richland Community College Attribute of Cube Root Function Exercises

4 questions show your work on paper clearly please. I upoaded the pages below

Name
Class
Date
10-2 CLASSWORK
Attributes of Cube Root Functions
If two functions are inverses of each other, they will undo each other. You can prove
that functions are inverses using the compositions f(g(x)) and g(x)).
Problem
Use composition of functions to determine whether f(x) = Vx+2
are inverses. Explain.
and g(x)=x3-2
Find the compositions/(g(x)) and g(x)).
$(8(x)) = 323-2+2
= X
$((x)) = (x+2)3 – 2
= 3×3
= X
Since f(g(x)) = x and g(/(x) = x, f(x) and g(x) are inverses.
Use composition to prove that f(x) and g(x) are inverses. Check your work.
$(x) = Vx+13; g(x) = (x -13)
1.
2. f(x) = x3 + 1; g(x) = 2x-1
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10-2 CLASSWORK (continued)
Attributes of Cube Root Functions
Because the domain and range of cube root functions are all real numbers, there is
no absolute maximum or minimum for the function. The same is true for cubic
functions, the inverse of cube root functions. However, you can find a local maximum
and minimum.
Problem
Graph the cube root function. What are the minimum and the maximum on the
given interval?
f(x) = {x + 4; [1, 8]
+y
8
6
4
2
8 6 4 -2
O
2
4
6
00
-2
-4
-6
-8
For the given interval, the graph rises as x increases, so the minimum and
maximum values of the function occur at the endpoints of the interval.
The minimum value on the interval is f(1) = 5 and the maximum value on
the interval is (8)=6.
Use the graph in the Problem above to analyze the maximum and minimum
values for the given interval.
3. (-8, 0]
4. (-1, 1]