Answered: Find the inverse ƒ-11x2 of each…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.CM: Cumulative Review Exercises

Problem 35CM

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Question

Find the inverse ƒ^-11x2 of each function (on the given interval, if specified).

ƒ1x2= 4e^5x

Expert Solution

Step 1

$G i v e n f u n c t i o n f (x) - f (x) = 4 e^{5 x} . . . . . . . . . . . . . . . . . . . . (1) F o r f i n d i n g t h e f^{- 1} (x), w e s o l v e f o r x - T a k i n g \ln o n b o t h s i d e s o f e q u a t i o n (1), \ln f (x) = \ln (4 e^{5 x}) \ln f (x) = \ln 4 + \ln e^{5 x} [\ln (a b) = \ln a + \ln b] \ln f (x) = \ln 4 + 5 x \ln e [\ln a^{b} = b \ln a] \ln f (x) = \ln 4 + 5 x (1) [\ln e = 1] \ln f (x) = \ln 4 + 5 x 5 x = \ln f (x) - \ln 4 x = \frac{\ln f (x) - \ln 4}{5} x = \frac{1}{5} \ln [\frac{f (x)}{4}] . . . . . . . . . . . . . . . . . (2)$

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