5. Algebraically determine whether each pair of functions are inverses using the composition of functions. (F.BF.B.4) h(x) = X-5.j(x) = 3x + 5 6. Rewrite the radical by extracting all possible roots and write your final answer in radical form. (N.RN.A.2) √81x¹y³z¹2

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Algebraic Concepts and Graphing Functions

#### Exercise c
**Task:** Write the domain and range of the inverse function \( g^{-1}(x) \). 
*(Standard: F.IF.B.5)*

#### Exercise d
**Task:** Complete the following table of values for this function. 
*(Standard: F.IF.A.2)*

| x    | \( g^{-1}(x) \) |
|------|-----------------|
| 0    |                 |
| 1/3  |                 |
| 1    |                 |
| 2    |                 |
| 3    |                 |

#### Exercise e
**Task:** Sketch the graph of \( g^{-1}(x) \) on the coordinate plane. 
*(Standard: F.IF.C.7.b)*

**Graph Description:**
The provided coordinate plane is a standard Cartesian coordinate graph with an x-axis and y-axis, each marked with unit intervals ranging from -8 to 8. Note that you are to graph the values you've calculated for \( g^{-1}(x) \).

#### Exercise 5
**Task:** Algebraically determine whether each pair of functions are inverses using the composition of functions. 
*(Standard: F.BF.B.4)*

Given functions:
\[ h(x) = \frac{x - 5}{3} \]
\[ j(x) = 3x + 5 \]

#### Exercise 6
**Task:** Rewrite the radical by extracting all possible roots and write your final answer in radical form.
*(Standard: N.RN.A.2)*

Given expression:
\[ \sqrt[8]{81x^{10}y^2z^{12}} \]

#### Exercise 7
**Task:** Combine like terms, if possible, and write your final answer in radical form. 
*(Standard: N.RN.A.2)*
Transcribed Image Text:### Algebraic Concepts and Graphing Functions #### Exercise c **Task:** Write the domain and range of the inverse function \( g^{-1}(x) \). *(Standard: F.IF.B.5)* #### Exercise d **Task:** Complete the following table of values for this function. *(Standard: F.IF.A.2)* | x | \( g^{-1}(x) \) | |------|-----------------| | 0 | | | 1/3 | | | 1 | | | 2 | | | 3 | | #### Exercise e **Task:** Sketch the graph of \( g^{-1}(x) \) on the coordinate plane. *(Standard: F.IF.C.7.b)* **Graph Description:** The provided coordinate plane is a standard Cartesian coordinate graph with an x-axis and y-axis, each marked with unit intervals ranging from -8 to 8. Note that you are to graph the values you've calculated for \( g^{-1}(x) \). #### Exercise 5 **Task:** Algebraically determine whether each pair of functions are inverses using the composition of functions. *(Standard: F.BF.B.4)* Given functions: \[ h(x) = \frac{x - 5}{3} \] \[ j(x) = 3x + 5 \] #### Exercise 6 **Task:** Rewrite the radical by extracting all possible roots and write your final answer in radical form. *(Standard: N.RN.A.2)* Given expression: \[ \sqrt[8]{81x^{10}y^2z^{12}} \] #### Exercise 7 **Task:** Combine like terms, if possible, and write your final answer in radical form. *(Standard: N.RN.A.2)*
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