Use the table below to fill in the missing values. x f(x) 0 6 1 7 4 9 3 1 2 5 23456 7 8 8 0 f(1) if f(x) = 5 then x = ƒ-¹ (7) = if f¹(x) = 7 then x = 89 58 9
Use the table below to fill in the missing values. x f(x) 0 6 1 7 4 9 3 1 2 5 23456 7 8 8 0 f(1) if f(x) = 5 then x = ƒ-¹ (7) = if f¹(x) = 7 then x = 89 58 9
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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![**Exercise: Understanding Functions and Inverse Functions**
Use the table below to fill in the missing values.
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & 6 \\
1 & 7 \\
2 & 4 \\
3 & 9 \\
4 & 3 \\
5 & 1 \\
6 & 2 \\
7 & 5 \\
8 & 8 \\
9 & 0 \\
\hline
\end{array}
\]
1. \( f(1) = \)
2. If \( f(x) = 5 \) then \( x = \)
3. \( f^{-1}(7) = \)
4. If \( f^{-1}(x) = 7 \) then \( x = \)
**Detailed Explanation:**
Make use of the table to answer the questions by looking for specific patterns and relations.
1. For \( f(1) \), simply check the value of \( f(x) \) when \( x = 1 \).
2. When given \( f(x) = 5 \), find the corresponding \( x \) value in the table.
3. For \( f^{-1}(7) \), identify the \( x \) value that maps to 7 using the definition of inverse functions.
4. For \( f^{-1}(x) = 7 \), similarly, identify the \( x \) given that 7 maps to it via the inverse of the function.
Utilize the concept of functions mapping inputs (x) to outputs (f(x)), and inverses reversing this mapping, to solve the problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d8b0e94-47ef-477e-9622-abc8b98247d8%2F17d494ae-d27b-49ca-bcec-4e6af9ffface%2F7fg0oxl_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise: Understanding Functions and Inverse Functions**
Use the table below to fill in the missing values.
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & 6 \\
1 & 7 \\
2 & 4 \\
3 & 9 \\
4 & 3 \\
5 & 1 \\
6 & 2 \\
7 & 5 \\
8 & 8 \\
9 & 0 \\
\hline
\end{array}
\]
1. \( f(1) = \)
2. If \( f(x) = 5 \) then \( x = \)
3. \( f^{-1}(7) = \)
4. If \( f^{-1}(x) = 7 \) then \( x = \)
**Detailed Explanation:**
Make use of the table to answer the questions by looking for specific patterns and relations.
1. For \( f(1) \), simply check the value of \( f(x) \) when \( x = 1 \).
2. When given \( f(x) = 5 \), find the corresponding \( x \) value in the table.
3. For \( f^{-1}(7) \), identify the \( x \) value that maps to 7 using the definition of inverse functions.
4. For \( f^{-1}(x) = 7 \), similarly, identify the \( x \) given that 7 maps to it via the inverse of the function.
Utilize the concept of functions mapping inputs (x) to outputs (f(x)), and inverses reversing this mapping, to solve the problems.
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