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1. For the given functions, state the range and find (f-¹)'(a) using the appropri- ate formula for the derivative of the inverse function. Do not find f-¹.

1. For the given functions, state the range and find (f-¹)'(a) using the appropri- ate formula for the derivative of the inverse function. Do not find f-¹.

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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Question
Solve 1 a ,b,c
ined in the problem. 1. For the given functions, state the range and find (f-¹)'(a) using the appropri- ate formula for the derivative of the inverse function. Do not find f-¹. (a) f(x) = x³ (b) f(x)=√x-2 (c) f(x) = 9-x² at a = 8 for 0≤x≤3 at a = 8 dy 2. For the given function, find the domain of y, dx (a) y = sin−¹(3x) V= (b) y = tan-¹(x³) and the domain of 3. Find the domain of the given logarithmic functions and solve the equation (a) log3x + log3(x + 2) = 1 (b) log₁0 (2x + 4) + log₁0 (x − 2) = 1 4. Find Show your work. Turn in at least TWO of the following proble dy dx (a) y = e cos x (b) y = xe ²x² - 4x (c) y = In (sin(x²)) (d) y = x ln(4x - 3) (e) y = ln(4- x³) dy 5. Find using logarithmic differentiation. Show your work. dx (x²+4)√4x − 1 (b) at a = 2 y = x cos x dy dx (c) y = x
Transcribed Image Text:ined in the problem. 1. For the given functions, state the range and find (f-¹)'(a) using the appropri- ate formula for the derivative of the inverse function. Do not find f-¹. (a) f(x) = x³ (b) f(x)=√x-2 (c) f(x) = 9-x² at a = 8 for 0≤x≤3 at a = 8 dy 2. For the given function, find the domain of y, dx (a) y = sin−¹(3x) V= (b) y = tan-¹(x³) and the domain of 3. Find the domain of the given logarithmic functions and solve the equation (a) log3x + log3(x + 2) = 1 (b) log₁0 (2x + 4) + log₁0 (x − 2) = 1 4. Find Show your work. Turn in at least TWO of the following proble dy dx (a) y = e cos x (b) y = xe ²x² - 4x (c) y = In (sin(x²)) (d) y = x ln(4x - 3) (e) y = ln(4- x³) dy 5. Find using logarithmic differentiation. Show your work. dx (x²+4)√4x − 1 (b) at a = 2 y = x cos x dy dx (c) y = x
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