**Function Composition** Given the function \( f(x) = \frac{5}{6}x - 5 \) and the function \( g(x) = 5x^2 + 4x + 7 \), determine each of the following: **Give your answer as an integer or a simplified fraction.** 1. Evaluate \( f(g(6)) \) \( f(g(6)) = \) [__________] 2. Evaluate \( g(f(8)) \) \( g(f(8)) = \) [__________] 3. Evaluate \( f\left(g\left(\frac{1}{5}\right)\right) \) \( f\left(g\left(\frac{1}{5}\right)\right) = \) [__________] 4. Evaluate \( f\left(f\left(\frac{1}{5}\right)\right) \) \( f\left(f\left(\frac{1}{5}\right)\right) = \) [__________] - *Question Help:* - [Video] - [Message instructor] **[Submit Question]** [Text input box for response]

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Function Composition**

Given the function \( f(x) = \frac{5}{6}x - 5 \) and the function \( g(x) = 5x^2 + 4x + 7 \), determine each of the following:

**Give your answer as an integer or a simplified fraction.**

1. Evaluate \( f(g(6)) \)

   \( f(g(6)) = \) [__________]

2. Evaluate \( g(f(8)) \)

   \( g(f(8)) = \) [__________]

3. Evaluate \( f\left(g\left(\frac{1}{5}\right)\right) \)

   \( f\left(g\left(\frac{1}{5}\right)\right) = \) [__________]

4. Evaluate \( f\left(f\left(\frac{1}{5}\right)\right) \) 

   \( f\left(f\left(\frac{1}{5}\right)\right) = \) [__________]

- *Question Help:*
  - [Video]
  - [Message instructor]

**[Submit Question]**

[Text input box for response]
Transcribed Image Text:**Function Composition** Given the function \( f(x) = \frac{5}{6}x - 5 \) and the function \( g(x) = 5x^2 + 4x + 7 \), determine each of the following: **Give your answer as an integer or a simplified fraction.** 1. Evaluate \( f(g(6)) \) \( f(g(6)) = \) [__________] 2. Evaluate \( g(f(8)) \) \( g(f(8)) = \) [__________] 3. Evaluate \( f\left(g\left(\frac{1}{5}\right)\right) \) \( f\left(g\left(\frac{1}{5}\right)\right) = \) [__________] 4. Evaluate \( f\left(f\left(\frac{1}{5}\right)\right) \) \( f\left(f\left(\frac{1}{5}\right)\right) = \) [__________] - *Question Help:* - [Video] - [Message instructor] **[Submit Question]** [Text input box for response]
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