Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
10th Edition
ISBN: 9781285464640
Author: Soo T. Tan
Publisher: Brooks Cole
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Chapter A, Problem 6E
To determine
To show: The function f and g are inverse of each other.
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Show that g(x) = x/(x-1) is equal to its inverse on the domain x-1 {x : x # l}.
Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval. f(x) = ∣x + 2∣, [−2, ∞)
Let k(x)=f(x)g(x)h(x). If f(x)=−2x−3,g(x)=−3x+3, and h(x)=−3x2+x+1, what is k′(1)?
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Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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- Show that the function fx)=ax is its own inverse for all real numbers a.arrow_forwardShow that f is strictly monotonic on the given interval and therefore has an inverse function on that interval. f(x) = (x − 4)2, [4, ∞)arrow_forwardLet f, g: R→R be defined byf (x) = {4x + 1 , if x ≥0, x , if x < 0} g(x) = {3x , if x ≥0 , x + 3 , if x < 0.} Find the inverse of f ◦g.arrow_forward
- Show that f(x) and g(x) are functions by showing that f(g(x)) =x and g(f(x) = x f(x) = (x-2)^2 g(x) = square root of x +2arrow_forwarddescribe the values of x that must be excluded from the domain of (f g)(x) based on the example below: f(x)=2x, g(x)=3x f(g(x))=f(3x) =2(3x)=6x F(g(x)=6x How do you determine the domain of the composition of these two functions (from the example given)?arrow_forwardSuppose f is an invertible function and f^-1 is its inverse. Explain how we can use the chain rule to differentiate f(f^−1(x)). Note: f^-1(x) is not 1/f(x)arrow_forward
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Inverse Functions; Author: Professor Dave Explains;https://www.youtube.com/watch?v=9fJsrnE1go0;License: Standard YouTube License, CC-BY