Use the given values to find (f-1)'(a). f( – 3) - 1, f'( – 3) - 2, а %— - 1 | (f-')'(a) = Preview TIP Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
Use the given values to find (f-1)'(a). f( – 3) - 1, f'( – 3) - 2, а %— - 1 | (f-')'(a) = Preview TIP Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
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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![### Inverse Function Derivative Calculation
To calculate the derivative of the inverse function \((f^{-1})'(a)\) using the provided values, follow these steps.
Given values:
\[ f(-3) = -1, \quad f'(-3) = -2, \quad a = -1 \]
To find:
\[ (f^{-1})'(a) \]
### Calculation:
Use the formula for the derivative of the inverse function:
\[ \left( f^{-1} \right)'(a) = \frac{1}{f'\left( f^{-1}(a) \right)} \]
Since \( f^{-1}(-1) = -3 \):
\[ f(-3) = -1 \]
We are given:
\[ f'(-3) = -2 \]
Thus,
\[ (f^{-1})'(-1) = \frac{1}{-2} = -\frac{1}{2} \]
### Answer:
\[ (f^{-1})'(-1) = -\frac{1}{2} \]
### Interactive Section:
Enter your answer below and press 'Preview' to check:
\[ (f^{-1})'(a) \, = \, \text{[ ]} \, \text{Preview} \]
#### TIP:
- Enter your answer as a number (like \( 5, -3, 2.2172 \)) or as a calculation (like \( \frac{5}{3}, 2^3, 5+4 \))
- Enter DNE for Does Not Exist, \( \infty \) for Infinity](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8315635d-2d20-4360-9a0a-b8ebc2e330cb%2F541f4d12-3261-4893-a780-1024444aff87%2Fueiqtgo_processed.png&w=3840&q=75)
Transcribed Image Text:### Inverse Function Derivative Calculation
To calculate the derivative of the inverse function \((f^{-1})'(a)\) using the provided values, follow these steps.
Given values:
\[ f(-3) = -1, \quad f'(-3) = -2, \quad a = -1 \]
To find:
\[ (f^{-1})'(a) \]
### Calculation:
Use the formula for the derivative of the inverse function:
\[ \left( f^{-1} \right)'(a) = \frac{1}{f'\left( f^{-1}(a) \right)} \]
Since \( f^{-1}(-1) = -3 \):
\[ f(-3) = -1 \]
We are given:
\[ f'(-3) = -2 \]
Thus,
\[ (f^{-1})'(-1) = \frac{1}{-2} = -\frac{1}{2} \]
### Answer:
\[ (f^{-1})'(-1) = -\frac{1}{2} \]
### Interactive Section:
Enter your answer below and press 'Preview' to check:
\[ (f^{-1})'(a) \, = \, \text{[ ]} \, \text{Preview} \]
#### TIP:
- Enter your answer as a number (like \( 5, -3, 2.2172 \)) or as a calculation (like \( \frac{5}{3}, 2^3, 5+4 \))
- Enter DNE for Does Not Exist, \( \infty \) for Infinity
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