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5. Consider the function f(x) = .5ln(1). Determine the domain and range of f. Find the inverse function to f and obtain its slope.

5. Consider the function f(x) = .5ln(1). Determine the domain and range of f. Find the inverse function to f and obtain its slope.

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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Check- 2x •5lm (14(@²2-1) itezx 15km 1- (@2xL ·1) 14e22 5km =.5 (2x) =x. 2 02% 1+6² tex 1+e2x 5. Consider the function f(x) = 5ln(1). Determine the domain and range of f. Find the inverse function to f and obtain its slope. f(x) = ₁5 lm (1+x) -₁5 ln (1-x) Df (-1<x<1) Note Rę (-∞,00) 1+2x²x+1 102x 4 fl= 15 1+2 Since of is monstone increasing over Of) an inverse. functur exists. het g(x) be the inverse fin -5m/1+g i-g. In ملا 2 6 1-g It dg dz Т-д argument to In must be > 0 727-1 1+2 1-2 20 =) x < 1 = = 20 =220 2x =e .5 + 1-x 22 i+g=e-ge 2x 22. g (1 + ²) = ²²²1 g=0²21 2x ite² 2e²* (1+²x) -2ex (2²²-₁) 2x (1+6²2) 2 2x (ite²x 220 ²² (1+0²² ²² +1) = 4e²zx de (1+6²x)2 (teen) 2
Transcribed Image Text:Check- 2x •5lm (14(@²2-1) itezx 15km 1- (@2xL ·1) 14e22 5km =.5 (2x) =x. 2 02% 1+6² tex 1+e2x 5. Consider the function f(x) = 5ln(1). Determine the domain and range of f. Find the inverse function to f and obtain its slope. f(x) = ₁5 lm (1+x) -₁5 ln (1-x) Df (-1<x<1) Note Rę (-∞,00) 1+2x²x+1 102x 4 fl= 15 1+2 Since of is monstone increasing over Of) an inverse. functur exists. het g(x) be the inverse fin -5m/1+g i-g. In ملا 2 6 1-g It dg dz Т-д argument to In must be > 0 727-1 1+2 1-2 20 =) x < 1 = = 20 =220 2x =e .5 + 1-x 22 i+g=e-ge 2x 22. g (1 + ²) = ²²²1 g=0²21 2x ite² 2e²* (1+²x) -2ex (2²²-₁) 2x (1+6²2) 2 2x (ite²x 220 ²² (1+0²² ²² +1) = 4e²zx de (1+6²x)2 (teen) 2
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