Consider two one-to-one functions f and g for which the following statements are true: • Domain of f is (0, 3). • Domain of g is [-1, 00). • Image of f is (-∞, ∞). • Image of g is (-2, 2]. •f(2) = 0 • g(0) = 1 (a) Why should we believe that f(1) # 0? because f is one to one and f(2) is already 0. . (b) Write the domain of f-: (c) Write the image of f-l: (d) Find the value of (f ~1 • g-1)(1) =

Q: 12 - y = | 4-x | Which of the following is the value set of the function? A) (-∞, 0) B) (-∞, ∞)…

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Q: Given a function and g(x) - 3(x- 1). how would the graph of. y-Ax) compare to the graph of y-Ag(x))?…

A: y=f(x)= 3x-3 is a straight line and graph is

Q: Let f be a function with the following known values f( – 1) = 1, f(0) = – 4, and f(3) = 5. %3D Let g…

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Q: Find the domain of the function f(x) 8 х—10 O R O R- {12} O R-{-10} O R- {10} O R-{14} Clear my…

A:

Q: The inverse of a relation r is r {(0, 0), (0, 1), (0, 2) }. Which of the following may be the…

A: Topic = Relation   The Inverse of a Relation is a set of ordered pairs that is the exact inverse of…

Q: Consider these functions. 1) Evaluate (f + g)(2). f(x) = 3x² – 5 g(x) = Vx - 2 A) -1 B) 0 C) 3 D) 7…

A: we have the given functions  f(x)=3x2-5 g(x)=x-2 1) (f+g)(2)=f(2)+g(2)…

Q: What is the domain of the function f (x) : (-1,0) U [1, 00) b. (-1,0] U (1, ∞) c. (-00, –1) U [0,1)…

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Q: 1) write the linear function f for which f(1)=3 and f(4)=0

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Let a, b be real numbers for which b > a. Let functions f,9,h be defined on a domain [a, b] in…

A: Solution is here

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: Use the graphs of f and g to evaluate g(f(2)) y 01 00 (-2,1) g (2,4) (2,-2) (4,3) X

A: We have to find out the value of g(f(2)) using the given graph.

Q: Find the domain. f(x) = 7x - 1 O {x[ x is a real number and x + 0.1428571 O {x[ x is a real number…

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Q: 3. State the domain and range of f(x) = –- 2 D:(-x,0] А. D: В. D:[-2,0) C. D:[1,0) D. R:(-0,-1]…

A: To state the domain and range of,fx=-12-x-1

Q: Define f(x ) = Vx2 +1 and g(x) = 2 – x2. State the domain of (f + g)(x ). x # v2, –v2 - [-1, 00)…

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Q: $42] B. (-∞0.42) C. (-∞,21] C

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Q: (-10,3) 23 (-2-1-0) -16 (-12,-3) (-8,0) (+3,-1)/ (-6,-5) 61 (1,0) (3,2) -6 (0, -1) (-4,-3) (5,0) y =…

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Q: en (1, 1) is a point on the base graph of f(x) = x5 and g(x) = -(x-1)6 +5, f would be moved to on…

A: The base point is given as (1, 1). The base function is given as f(x)=x5.

Q: Sketch the graph of the function. f(x) = In(|x|) 3 U

A: Given  f(x)=ln(|x|)write as piece wise function f(x)=ln(-x)     for x < 0ln(x)         for x >…

Q: Suppose a, b, c, and d are integers, and that a is negative and odd, b is positive and even., c is…

A: Ans:Suppose a,b,c and d are integers a is negative and odd, b is positive aand even, c is positive…

Q: Which of the following is the domain of the function g(x) 2-x 0(-00,2 O (-00, 0) O [0, ∞0) O (-0, 2)

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Q: Suppose that f(r) is a function with f(4) 4 and f(8) 4. Determine which choice best describes the…

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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.