78 CFinding an Inverse Function Algebraically In Exercises71-80, find the inverse function of f algebraically. Use agraphing utility to graph both f and f-¹ in the sameviewing window. Describe the relationship between thegraphs.72. f(x) = 3x74. f(x) = x³ + 176. f(x) = x², x ≥ 078. f(x)=√16-², -4 ≤x≤0

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College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Functions And Their Graphs

Section2.7: Inverse Functions

Problem 99E

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Finding an Inverse Function InformallyIn Exercises 7–14, find the inverse function off informally. Verify that f( f −1(x)) = x andf −1( f(x)) = x.7. f(x) = 6x 8. f(x) = 13x9. f(x) = 3x + 1 10. f(x) = x − 3211. f(x) = x2 − 4, x ≥ 012. f(x) = x2 + 2, x ≥ 013. f(x) = x3 + 114. f(x) = x54
Composition with Inverses In Exercises 85–88,use the functions f(x) = x + 4 and g(x) = 2x − 5 tofind the function.85. g−1 ∘ f −1 86. f −1 ∘ g−187. ( f ∘ g)−1 88. (g ∘ f)−1
Finding an Inverse Function InformallyFind the inverse function of f(x) = 4x. Then verify that both f( f −1(x)) and f −1( f(x))are equal to the identity function.
finding the derivate of the function, image
True or False? In Exercises 125 and 126, determinewhether the statement is true or false. Justify youranswer.125. Relative to the graph of f(x) = √x, the graph of thefunction h(x) = −√x + 9 − 13 is shifted 9 units tothe left and 13 units down, then reflected in the x-axis.126. If f and g are two inverse functions, then the domainof g is equal to the range of f
Verifying Inverse Functions In Exercises 21–32, verify that f and g are inverse functions (a) algebraically and (b) graphically. 21. f(x) = x − 5, g(x) = x + 5 22. f(x) = 2x, g(x) = x 2 23. f(x) = 7x + 1, g(x) = x − 1 7 24. f(x) = 3 − 4x, g(x) = 3 − x 4 25. f(x) = x3, g(x) = √ 3 x 26. f(x) = x3 3 , g(x) = √ 3 3x 27. f(x) = √x + 5, g(x) = x2 − 5, x ≥ 0 28. f(x) = 1 − x3, g(x) = √ 3 1 − x 29. f(x) = 1 x , g(x) = 1 x 30. f(x) = 1 1 + x , x ≥ 0, g(x) = 1 − x x , 0 < x ≤ 1 31. f(x) = x − 1 x + 5 , g(x) = −5x + 1 x − 1 32. f(x) = x + 3 x − 2 , g(x) = 2x + 3 x − 1
Consider a function f(x). State the condition for the function to have an inverse and how you can check if the condition holds. State also the relationship between the graphs of f(x) and f-1(x).
Explain how to find the inverse of a function from its equation. Use an example to demonstrate the steps.
How do you find the inverse of a function algebraically?
How do you find the domain for the composition of two functions, fg ?
Using a Table to Determine an Inverse FunctionIn Exercises 33 and 34, does the function have an inversefunction?
Using a Table to Find an Inverse Function InExercises 35 and 36, use the table of values for y = f(x)to complete a table for y = f −1(x).

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