지되지 g[x) f'(x) g '(x) 3 19 8 3 4-3 3 2 -5 f(g(x)), x = 4 24 -10 -40 CO

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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how do i solve? i asked this question before but was given the wrong answer of 1 which is not correct

The image presents a problem involving composed functions and their derivatives. Here is the transcription and explanation suitable for an educational website.

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### Calculus Problem: Evaluating Composed Functions

Consider the following table that provides values for functions \( f \) and \( g \), as well as their derivatives \( f' \) and \( g' \), at specific points:

| \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) |
|:------:|:-------:|:--------:|:--------:|:---------:|
| 3      | 1       | 9        | 8        | 3         |
| 4      | -3      | 3        | 2        | -5        |

#### Problem:
Calculate \( f(g(x)) \) for \( x = 4 \).

Options:
- (A) 24
- (B) -10
- (C) -40
- (D) 8

#### Solution:
To find \( f(g(x)) \) when \( x = 4 \):

1. First, identify \( g(4) \) from the table, which is 3.
2. Next, find \( f(g(4)) \) which translates to \( f(3) \).
3. From the table, \( f(3) \) is given as 1.

Therefore, \( f(g(4)) = f(3) = 1 \).

None of the provided options (24, -10, -40, 8) match the correct answer, which is 1. It seems there may be a mistake in the options given.

--- 

This transcription provides a step-by-step solution to the problem based on the given table.
Transcribed Image Text:The image presents a problem involving composed functions and their derivatives. Here is the transcription and explanation suitable for an educational website. --- ### Calculus Problem: Evaluating Composed Functions Consider the following table that provides values for functions \( f \) and \( g \), as well as their derivatives \( f' \) and \( g' \), at specific points: | \( x \) | \( f(x) \) | \( g(x) \) | \( f'(x) \) | \( g'(x) \) | |:------:|:-------:|:--------:|:--------:|:---------:| | 3 | 1 | 9 | 8 | 3 | | 4 | -3 | 3 | 2 | -5 | #### Problem: Calculate \( f(g(x)) \) for \( x = 4 \). Options: - (A) 24 - (B) -10 - (C) -40 - (D) 8 #### Solution: To find \( f(g(x)) \) when \( x = 4 \): 1. First, identify \( g(4) \) from the table, which is 3. 2. Next, find \( f(g(4)) \) which translates to \( f(3) \). 3. From the table, \( f(3) \) is given as 1. Therefore, \( f(g(4)) = f(3) = 1 \). None of the provided options (24, -10, -40, 8) match the correct answer, which is 1. It seems there may be a mistake in the options given. --- This transcription provides a step-by-step solution to the problem based on the given table.
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