Verify that f has an inverse function. Then use the function f and the given real number a to find (f)(a). (Hint: See Example 1. If an answer does not exist, enter DNE.) F(x) = x - 4, a = 121 Step 1 The given function is f(x) = x- 4. Differentiate f(x) with respect to x. F"(x) = Step 2 The function f(x) = 3x is always non-negative non-negative on the domain of f(x). Therefore, f(x) is is monotonic on the domain of x and the inverse of the function exists. Step 3 To find f(x), let y = f(x) and solve for x, y = x - 4 x = (y + 4) Interchange x and y in the expression for x. y = (x + 4) Find f-(x) by replacing y with f-1(x). rx) = (x + 4)

Verify that f has an inverse function. Then use the function f and the given real number a to find (f)(a). (Hint: See Example 1. If an answer does not exist, enter DNE.) F(x) = x - 4, a = 121 Step 1 The given function is f(x) = x- 4. Differentiate f(x) with respect to x. F"(x) = Step 2 The function f(x) = 3x is always non-negative non-negative on the domain of f(x). Therefore, f(x) is is monotonic on the domain of x and the inverse of the function exists. Step 3 To find f(x), let y = f(x) and solve for x, y = x - 4 x = (y + 4) Interchange x and y in the expression for x. y = (x + 4) Find f-(x) by replacing y with f-1(x). rx) = (x + 4)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.1: Inverse Functions

Problem 55E

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