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Several statements about a differentiable, invertible function f(r) and its inverse f-(z) are written below. Mark each statement as either "TRUE" or "FALSE" (no work need be included for this question). 1. If f(T) = 2022 then 7 = f-'(2022). 2. If f is increasing on its domain, then f-1 is also increasing on its domain. 3. The domain of f-1 is the range of f. 4. If r is in the domain of f-l then f(f"(x)) = = r. 5. If f is concave up on its domain then f-1 is concave up on its domain. (Hint: think about the examples f(r) = er and f-1(1) = In r.)

Several statements about a differentiable, invertible function f(r) and its inverse f-(z) are written below. Mark each statement as either "TRUE" or "FALSE" (no work need be included for this question). 1. If f(T) = 2022 then 7 = f-'(2022). 2. If f is increasing on its domain, then f-1 is also increasing on its domain. 3. The domain of f-1 is the range of f. 4. If r is in the domain of f-l then f(f"(x)) = = r. 5. If f is concave up on its domain then f-1 is concave up on its domain. (Hint: think about the examples f(r) = er and f-1(1) = In r.)

Calculus: Early Transcendentals
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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Several statements about a differentiable, invertible function f(r) and its inverse f-(z) are written below. Mark each statement as either "TRUE" or "FALSE" (no work need be included for this question). 1. If f(T) = 2022 then 7 = f-'(2022). 2. If f is increasing on its domain, then f-1 is also increasing on its domain. 3. The domain of f-1 is the range of f. 4. If r is in the domain of f-l then f(f"(x)) = = r. 5. If f is concave up on its domain then f-1 is concave up on its domain. (Hint: think about the examples f(r) = er and f-1(1) = In r.)
Transcribed Image Text:Several statements about a differentiable, invertible function f(r) and its inverse f-(z) are written below. Mark each statement as either "TRUE" or "FALSE" (no work need be included for this question). 1. If f(T) = 2022 then 7 = f-'(2022). 2. If f is increasing on its domain, then f-1 is also increasing on its domain. 3. The domain of f-1 is the range of f. 4. If r is in the domain of f-l then f(f"(x)) = = r. 5. If f is concave up on its domain then f-1 is concave up on its domain. (Hint: think about the examples f(r) = er and f-1(1) = In r.)
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