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 5E
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 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.
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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 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)?arrow_forward
- Let k(x)=f(x)g(x)h(x). If f(x)=−4x−3,g(x)=2x+2, and h(x)=4x^2+2x+2, what is k′(x)?arrow_forwardProve that the function given by f(x) =x3-3x2+3x-100 is increasing in Rarrow_forwardThe function f : R → R defined by the formula f(x) = 3x − 5 for all x ∈ R was shown to be one-to-one in Example 2 and onto in Example 4. Find its inversefunction.arrow_forward
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