Use composition of functions to determine whether f(x) and g(x) are inverses of each other. Show all work for full credit. 4 f (x) 5* +1 5x – 5 9 (x) 4

Q: 2. Find the inverse of the function and the domain and range of both f(x) and f-(x). 4x + 15 f(x) x…

A: Topic = Functions

Q: a. What is f'(-1)? b. What is the inverse of the function? c. Find (f-1)' (1)

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Q: Which is the inverse of the function f(x) = 2 – 22? of1(2) = -글z + 1 O f1(x) = -+ o f(2) = Of '(x) =…

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Q: Express the function,h(x) = |3x - 4|as a composition of two functions f and g so that h(x) = (f ∘…

A: h(x) = |3x - 4| To write h(x) as a composition of two functions f and g so that h(x) = (f ∘ g)(x)…

Q: 18. Are these two functions inverses of each other? Explain by showing your work. (Hint: f(g(x))and…

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Q: Determine the domain of the function 2x f(x) = 1+ x Is the function f injective? If the answer is…

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Q: Given the function f(x)= { (1,8), (2,16), (3,24), ( 4,32)}, Find the inverse of f-1(x) = {       }

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Q: The function ​f(x)=[(3x)/(8x-1)] is​ one-to-one. ​(a) Find its inverse and check your answer.​

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Q: Express h(x) = (x2 - 3x + 7)9 as a composition of two functions f and g such that h(x) = ( f ∘…

A: To Determine:  Express h(x)  as a composition of two functions f and g such that h(x) = ( f ∘ g)(x).…

Q: Find the inverse function of f(x) : x – 8 – 5. Specify the domain for f-'(x) Domain of f-1(x) using…

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Q: Find the inverse function of f(x) – Va + 3. Specify the domain for f-1(x) f'(x): x² – 6x + 9 Domain…

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Q: E piecewise function, evaluate f(-2). -5x + 4 x < f(x) = %3D -3x +3 x

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Q: The function f (x) is defined below. What is the end behavior of f (x)? f (x) = -1120x + 120x2 -…

A: Given, f(x) = -1120x + 120x2 -10x4 + 80x3 +1280

Q: 13. Use the Inverse Function Property to show that f(x) 1 is the inverse of 1 g(x) x - 2 + 2. %3D

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Q: Let f and g be inverse functions that are differentiable for all æ. If f(-5) = 7 and g'(7) = 3,…

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Q: 3 Friday Find the inverse of f(x) =x- 2 and name a coordinate on f(x).

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Q: 3x Determine the domain of the function h(x) = x(* - 25) , x *

A: Given query is to find the domain of the function.

Q: 3x + 2x. Let f(x) = 4x + 4 and g(x) After simplifying, (f + g)(x)

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Q: 2. Find the inverse of the function, and prove using composition that the two are inverses of each…

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Q: Drag a function or an interval into each box to correctly complete the statement. When the domain of…

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Q: Let f and g be inverse functions that are differentiable for all a. If f(-5) = 7 and g'(7) = 3,…

A: If f and g are inverse function then f∘g(x)=x           and       g∘f(x)=x

Q: 3) Do the following operations of functions. a) f(x) = x² + 3x , g(x)= 8x +9 find (f+g)(4) = ? b)…

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Q: Use composition of functions to determine whether f(x) and g(x) are inverses of each other. Show all…

A: The given functions are f(x)=45x+1 and g(x)=5x-54

Q: 9. Find the difference quotient for the function g(x)=- then simplify. x-1'

A: The difference quotient will be given by: [g(x+h) - g(x)] / h

Q: The one-to-one function f is defined below. f (x) = V3x-8 1 Find f'(x), where f' is the inverse of…

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Q: Use compositions of functions to decide whether or not the functions are inverses of each other. 5)…

A: Both are inverse of each other if their composition gives identity.

Q: 3 3 For the functions f(x) = and g(x) = -+ 4, find f(g(x)) and g(f(x)), hence or otherwise determine…

A: Given functions: f(x)=3x-4g(x)=3x+4 Function 'g(x)' is said to be inverse of function 'f(x)' only if…

Q: Prove whether or not the given functions are inverses. 9) f(x) = x - 5 g(x) = x +5 10) f(x) = Vx + 3…

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Q: 3 Consider the functions f(x) = x° - 5 and g(x) = Vx +5. (a) Find f(g(x)). (b) Find g(f(x)). (c)…

A: Given, f(x)=x3-5g(x)=x+53

Q: he function f is defined by f (x) = 2x° + 3x - 2. If g is the inverse function of f and g(-7) = -1,…

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Q: 3. Write the function F (x) = x3+6 as a composition of three or more non- x3 identity functions.

A: The given function is, Fx=x3+6x3-9

Q: 4. Consider the function if x > 0 {2 if a < 0 g : R – R, g (x) = -2x2 Is this function bijective?…

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Q: The function f is defined by f(x) = -2x³ - x² - 6x and the point (-1,7) is on the graph of f. If f¹…

A: Given is the function f(x)=-2x3-x2-6x and point (-1,7) is on graph f. f-1 is the inverse of f. We…

Q: B. Using the definition of inverse function, verify if the following pairs of function are inverse…

A: Steps to find inverse: Step 1: Put function as y.  Step 2: switch x and y.  Step 3: Find y.  Step 4…

Q: C. Use the composition of function to verify if the given pairs are inverses of each other. 1. S(x)…

A: Note: According to our guidelines we can solve only first three subparts and rest can e…

Q: The function f is defined by f (x) = -x³ + 3x² – 3x and f(2) =-2. If g is the inverse function of f,…

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Q: Express the function in the form fog. (Use non-identity functions for fand g.) F(x) = (7x + x2)4…

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Q: 18. Are these two functions inverses of each other? Explain by showing your work. (Hint: f(g(x))and…

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Q: State whether the function f has an inverse. Iff 1 exists, find the rule for f-1(x) and show that…

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Q: Consider the function f(x)=x3+x+1. Let's suppose that it has an inverse g so that g(f(x))=x. What is…

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Q: Are the following functions the inverse of each other? (Hint: Use composition function) f(x) = 6x-1…

A: Use simple steps for inverse

Q: Determine if the functions in each pair are equivalent. Provide mathematical proof or justification…

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Q: Express the function,h(x) = (2x - 5)3 as a composition of two functions f and g so that h(x) = (f ∘…

A: Given, hx=2x-53

Q: - Find the composition of the function. f(a) = 2° and g(x) = V Find g(f(x)).

A: Composition

Q: 3 (5) For the functions f(x) = and g(x) =-+ 4, find f(g(x)) and g(f(x)), hence or 3 X - 4 otherwise…

A: We use the definition of composition of functions and inverse of a function to find the answer of…

Q: Find the composit function (h(g(x). Simplify your answer. g(x)=x2+4x-2 h(x)=x2-3x+1

A: Given: g (x) = x 2 + 4 x – 2 h (x) = x 2  – 3 x + 1.   To find: The composite function h (g (x)).

Q: Express the function,h(x) =1/(4x + 5) as a composition of two functions f and g so that h(x) = (f ∘…

A: here given as hx=fogx=14x+5

Q: Determine whether the function y= -x5 + x³ – 1 is even, odd, or neither. Justify your ans we r.

A: A function is said to be even function if y(-x)=y(x) and it is said to be odd function if…