In an algebra book you read the following definition: The function g : Y → X is the inverse of the function f : X → Y if the two diagrams in Figure 1.9 commute. Is this any different from our definition of inverses? Can you draw one diagram—with four nodes and five arrows—that is commutative if and only if g is the inverse of f?

Q: Show that the following functions are inverses of each other: 2х - 1 3x +1 k(x) = and h(x) = x+3 2-x

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Q: Suppose Ax) and g(x) are inverses of each other. If A-1) =3 and g(2) =-5. Find the following, if 18.…

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Q: 24) Use f (x) = and g(x) = x2 +x for the following. Simplify your answer. a) Find (g f(9) b) Find f…

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Q: Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each…

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Q: Does the graph represent a function that has an inverse function? A) No A) No B) Yes B) Yes

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Q: By definition, if f and g are inverses of one another, then their composition acts like the identity…

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Q: (Hint: To determine if functions are inverses of each other, calculate (f • g)(x) and (g º f)(x).)…

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Q: 1. Show that the inverse of a function is unique. If a function has an inverse, then it only has…

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Q: 1. Find the inverse of the following function: f(x) = x² + 2x-4. Restrict the domain of f(x) such…

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Q: Verify that the functions are inverses by showing that f. g and go fare the identity function. f(x)…

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Q: If the two functions are inverses, which of the following statements correctly verifies this? f(x) =…

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Q: Exercise 8.7.9. In each case, use Definition 8.7.7 to determine whether g is an inverse of f. (a) f:…

A: 1. Given  f(x) = 9x - 6 g(y) = y+69 So fgy = 9y+69 - 6 = yandgfx = 9x - 6 + 69  =  x Hence g is a…

Q: 4.) Consider the function f(x) = x - 1 a.) Find f(-6) b.) Sketch a graph of the function EAJ…

A: The function is given by f(x) = 23x-1 To evaluate: The value of x if f(x) = 1.