Suppose that the range of g lies in the domain of ƒ so that the composition ƒ ∘ g is defined. If ƒ and g are one-to-one, can any-thing be said about ƒ ∘ g? Give reasons for your answer

Q: If f:X → Y and g:Y → Z are one-to-one functions, then the composition f •g is one-to-one function.

A: f:X→Y and g:Y→Z are one-to-one function

Q: Let function f be defined by f (x) = x2 Use the graph of f for ε = 0.3 to determine δ > 0 such that…

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Q: Suppose that the function f is defined, for all real numbers, as follows. 3x-1 if x<-1 f (x) =- -x+1…

A: Given: The Piece wise function f(x)=-3x-1If x&lt;-1-x+1If x≥-1 To find: Graph the given piece wise…

Q: If f is an even function, then f(-x) = ................. The graph of an even function is symmetric…

A: A function f is said to be an even function if And the graph of even function is symmetric with…

Q: Sketch, on the same coordinate plane, the graphs of f for the given values of c. (Make use of…

A: Given the function f(x)=-x2+c;  c=-5,1,5. We need to sketch the graph Let us sketch for f(x)= -x2-5.…

Q: Suppose that the function f is defined, for all real numbers, as follows. f (x) = x - 4      if x…

A: To graph the function f and determine whether or not the function is continuous. f(x)=x-4       if…

Q: Consider the function f(x) whose graph is shown below. What can be said about the limit of f(x) a.…

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Q: Let g(x)= Find the domain of g(x).

A: The domain of a function is the set of all possible inputs for the function

Q: Suppose that the range of g lies in the domain of ƒ so that thecomposite ƒ   g is defined. If ƒ and…

A: Composite function is usually a function which is written inside another function.

Q: Suppose that the function f is defined, for all real numbers, as follows. -x+2 if x 1 Graph the…

A: The given function,fx=-x+2if x≤15x-2if x&gt;1

Q: (x)=2x+1 and g(x)=x2-1. What is the composition (f of g)(x)?

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Q: Sketch the graph of the function and use it to determine the values of a for which limit of f(x)…

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Q: Suppose f and g are both one-to-one functions, and let h be the composition f and g; that is, h = f…

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Q: Suppose that g is an even function of x and h is an odd function of x. Show that if g(x) + h(x) = 0…

A: Consider that g(x) is the even function. Then, g(-x)=g(x) for all the value of x. Consider that h(x)…

Q: The graph of f(1) is given below. Select each true statement about the continuity of f(z) at = 0.…

A: From the graph: f(0) = -1 limx→0 f(x)=-3

Q: Consider functions f and g such that composite gof is defined and is one-one. Are f and g both…

A: Given f and g such that composite gof is defined and is one-one.

Q: Let f(x) = /1– x and g(x) = . Determine the following composition and its domain. g° g

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Q: Sketch, on the same coordinate plane, the graphs of f for the given values of c. (Make use of…

A: Consider the function: fx=x+c for c=-3,1,3. Plot the graph of fx.   Let gx=x First plot the graph of…

Q: 6. Let g(x) = Find the domain of g(x).

A: Topic = Functions   As per guidelines , At  a time only one question can be answered. please repost…

Q: Suppose the function f has a domain set of all real numbers. Given below is the graph of f(x). f'(x)…

A: We have to find the graph if the function f(x).

Q: The notation f° g, called the, function f with g, is defined by (f° g)(x) = of the

A: We have to fill in the blanks: The notation f∘g called the _________ of the function f with g, is…

Q: The graph of a function f is given in Figure 3.5. If f is a polynomial of degree 3, then the values…

A: for given graph: let the polynomial equation be y= ax^3+bx^2+cx+d x=0,y=0 .....from graph putting…

Q: Use the given graph of f to find a number ô such that if |x - 1| < 8 then If(x) – 1| < 0.2 8 = 1.2 1…

A: We will use the defination of limit in order to solve the given problem.

Q: Suppose that f : A → B and g : B → C are both injective functions, prove that the function go f : A…

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Q: Suppose that the function g is defined, for all real numbers, as follows. if x+0 -1 g(x) = -2 if x=…

A: for the given function

Q: Let 2x - x if 0 4 (a) For each of the numbers 2, 3, and 4, dctcrmine whether g is continuous from…

A: We are given                 . For (a), For each numbers 2, 3, and 4, we need to determine whether g…

Q: Suppose that the function g is defined, for all real numbers, as follows. if x+ -1 g (x) = - 1 if x…

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Q: Let X = {a, b, c, d} and Y = {e, f, g}. Define functions Fand G by the arrow diagrams below. Domain…

A: topic - sets and relations

Q: If ƒ(a - x) = ƒ(a + x), show that g(x) = ƒ(x + a) is an even function.

A: Given that ƒ(a - x) = ƒ(a + x)To show that g(x) = ƒ(x + a) is an even function.

Q: Suppose that the functions g and ƒ are defined as follows. g (x) = (6+x)(-4+x) f(x) = -5-x (a) Find…

A: GIVEN     gx =6+x-4+x                     fx=-5-x

Q: ) Suppose that S is an infinite set and f : N → S is onto S. Explain how to define a function g : N…

A: Suppose S is an infinite set and f:N→S is onto to S. The objective is to define a function g:N→S is…

Q: if r < 3 12 if a 3' limits do not exist, enter Ø as your answer. For the function f(x)% = evaluate…

A: The given function,       f(x)=xif x&lt;312xif x≥3

Q: If f is an even function, then f(-x) =_________ . The graph of an even function is symmetric with…

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Q: If f is C2 on an interval prove that f(2 + k) – 2/(2) + {(z =A) = r"(2). - lim h-0 h2 = f"(x). The…

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Q: Suppose that B is a subset of A. Specify a one-to-one function whose domain is B and whose range is…

A: suppose that B is a subset of A claim- to find a one-to-one function whose domain is B and range is…

Q: function g : Z → Z is defined as g(n) = |n| + 1. Show that this function is not injective and not…

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Q: Suppose f and g are functions with domain R. If both f and g are even but f + g is odd, then prove…

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Q: Find the composition g(f(x)) and describe its domain. f(x) : 2 and g(x) = x+1 x-1 g(f(x)) =

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Q: Suppose that the functions fand g are defined as follows. f4) = 3x-4 g(x) =/4x-5 %3D Find f-g and…

A: Given functions are fx=3x-4gx=4x-5

Q: Suppose that the functions fand g are defined as follows. f(x) = ,x#0 g(2) =x-s Find the…

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Q: Suppose that the function g is defined, for all real numbers, as follows. 3 if x #-2 g (x) = 4 if x…

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Q: Suppose that the functions h and g are defined as follows. h (x) =x+4 g (x) = (x+1)(x+2) )(-3). (a)…

A: Given : hx = x+4gx = x+1x+2

Q: Given a function f and a subset A of its domain, let f(A)represent the range of f over the set A;…

A: We have got a given function  f and a subset A of its domain, let f(A)   represent the range of f…

Q: Give an example of a function f : A4 → S6 that is not a homomorphism. Justify your answer

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Q: Suppose that the functions f and g are defined as follows. f (x) = (x+ 3)(x+3) g(x) = -x- 5

A: If there is a question that has more than 1 question and questions other than the first has subpart,…

Q: Given a function f and a subset A of its domain, let f(A)represent the range of f over the set A;…

A: To show that  for an arbitrary function g : R → R, it is always true that g(A ∩ B) ⊆ g(A) ∩ g(B)…

Q: _The graph of the function f is shown below. Which of the statements must be FALSE? a Graph of f…

A: The graph of the function are

Q: If f is an odd function and g is an even function, show that the composite functions f ∘ g and g ∘ f…

A: Given that f is an odd function and g is an even function that is f-x=-fxg-x=gx

Q: Suppose that B is a subset of A. Specify a one-to-one function whose domain is B and whose range is…

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