Evaluate each expression using the values given in the table. - 2 - 1 - 3 -3 2 3 f(x) g(x) - 9 - 6 - 1 3 9. 3 - 1 3 a. (fo g)(1) d.(g o f)(0) b. (fo g)(- 1) e. (go g)(- 2) c. (go f)( – 1) f. (fo f)(- 1) a. (fo g)(1) =
Evaluate each expression using the values given in the table. - 2 - 1 - 3 -3 2 3 f(x) g(x) - 9 - 6 - 1 3 9. 3 - 1 3 a. (fo g)(1) d.(g o f)(0) b. (fo g)(- 1) e. (go g)(- 2) c. (go f)( – 1) f. (fo f)(- 1) a. (fo g)(1) =
Calculus: Early Transcendentals
8th Edition
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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![**Evaluate each expression using the values given in the table.**
\[
\begin{array}{|c|c|c|}
\hline
x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline
f(x) & -9 & -6 & -3 & -1 & 3 & 6 & 9 \\
\hline
g(x) & 9 & 3 & 0 & -1 & 0 & 3 & 9 \\
\hline
\end{array}
\]
**Expressions to Evaluate:**
a. \( (f \circ g)(1) \)
b. \( (f \circ g)(-1) \)
c. \( (g \circ f)(-1) \)
d. \( (g \circ f)(0) \)
e. \( (g \circ g)(-2) \)
f. \( (f \circ f)(-1) \)
### Solution Explanation:
To evaluate these expressions, we must understand composition of functions, denoted by \( (f \circ g)(x) = f(g(x)) \). This means we first apply \( g \) to \( x \), and then apply \( f \) to the result.
**a. \( (f \circ g)(1) \)**
1. Find \( g(1) \):
- From the table, \( g(1) = 0 \).
2. Find \( f \) of the result from step 1:
- \( f(g(1)) = f(0) \).
- From the table, \( f(0) = -1 \).
3. Therefore, \( (f \circ g)(1) = -1 \).
Repeating similar steps, one can evaluate all the other expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49360a23-9f24-445c-a223-e7141e33e2c6%2F0ef7de55-33f3-48de-a864-fd728565182c%2F8wsg8i_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate each expression using the values given in the table.**
\[
\begin{array}{|c|c|c|}
\hline
x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\
\hline
f(x) & -9 & -6 & -3 & -1 & 3 & 6 & 9 \\
\hline
g(x) & 9 & 3 & 0 & -1 & 0 & 3 & 9 \\
\hline
\end{array}
\]
**Expressions to Evaluate:**
a. \( (f \circ g)(1) \)
b. \( (f \circ g)(-1) \)
c. \( (g \circ f)(-1) \)
d. \( (g \circ f)(0) \)
e. \( (g \circ g)(-2) \)
f. \( (f \circ f)(-1) \)
### Solution Explanation:
To evaluate these expressions, we must understand composition of functions, denoted by \( (f \circ g)(x) = f(g(x)) \). This means we first apply \( g \) to \( x \), and then apply \( f \) to the result.
**a. \( (f \circ g)(1) \)**
1. Find \( g(1) \):
- From the table, \( g(1) = 0 \).
2. Find \( f \) of the result from step 1:
- \( f(g(1)) = f(0) \).
- From the table, \( f(0) = -1 \).
3. Therefore, \( (f \circ g)(1) = -1 \).
Repeating similar steps, one can evaluate all the other expressions.
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