Suppose that B is a subset of A. Specify a one-to-one function whose domain is B and whose range is a subset of A.By doing this you will show that |B| < |A||

Q: Suppose that f (x) is a function with f (0) 1 and f' (0) = 3.1 If g(x) = (f (x))³ , then what is the…

A: We find value of g'(0)

Q: Consider the following function. f (x) = In (1 + 2x), a = 5, n = 3, 4.6 < x < 5.4

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Q: Suppose that f is an even function and g is an odd function (both with domain R) . If f(3)=4 and…

A: Given, f is an even function and g is an odd function. f(3)=4 and g(-3)=5 Identity: For even and odd…

Q: Given that the domain of a one-to-one function f is [0, ∞) and the range of f is [0, 4), state the…

A: Definition of one to one and inverse function:

Q: Suppose that the functions f and g are defined as follows

A: Given functions:

Q: If g(x) is an even function, then f(g(x)) is even. Is this false or true.

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Q: Suppose f is a one-to one function. If f(4) = 3 , then f(3) is %3|

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Q: If A and B are finite, show that the set of all functions f: A B is finite.

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Q: 1. If f(x) = x + 5 and g(x) = x – 5, (a) f(g(x)) = (b) g(f(x)) (c) Thus g(x) is called an function…

A: Note: According to our answering guidelines we have to solve only one question (if multiple…

Q: Draw a graph of the function f, and determine the intervals of which f is increasing and on which f…

A: A function is said to be increasing if for the increasing values of input, the corresponding values…

Q: Find and classify the discontinuities of the following function as removable or nonremovable. If a…

A: Consider the function    ux=x2-9x-5 Removable discontinuity:-   A discontinuity at a point x=a  is…

Q: 77. If f is an odd function and g is an even function, show that the composite functions f°g and gof…

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Q: 5. Suppose f(x) is an odd function. Prove that g(x)=f(x)| is an even function.

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Q: Invent an interesting and original piecewise function, p(x). For the function you invented in…

A: A piecewise function is a function where more than one formula is used to define the output. Each…

Q: Show that if f is one-to-one then f is strictly monotonous,. it means : f is  either strictly…

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Q: Suppose that f (x), g(x), and h(x) are functions such that f (x) is Θ(g(x)) and g(x) is Θ(h(x)).…

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Q: If f(x) = x +2 and x = -3, then slop function is

A: Given f(x)= x+(9/x) and x=-3. We need to find the slope function.

Q: A function for which f(x) = f( - x) for all x in the domain of f is called a(n) ____function.

A: The types of functions help to fill the given blank. The definition that consists of the terms f(x)…

Q: Draw a graph of the function f, and determine the intervals of which f is increasing and on which f…

A: Draw a graph of the function f, and determine the intervals of which f is increasing and on which f…

Q: Draw a rough sketch of a function, f, that satisfies all of the following simultaneously:…

A: Suppose function is  fx=ax3+bx Since the function is odd so, it contains only odd power of x. Then,…

Q: Create a graph of the following function to determine whether it is continuous on its domain. S-a +…

A: From the basics of Limits and Continuity

Q: Sketch the graph of a function that satisfies all of the given conditions. f'(0) = f'(2) = f'(4) =…

A: gi&lt;x&lt;4ven:f'0=f'2=f'4=0f'x&gt;0if x&lt;0 or2&lt;x&lt;4f'x&gt;0ifx&gt;4 or 0&lt;x&lt;4f''x&gt;0…

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

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Q: Prove that if f and g are even functions, then fg is also an even function.

A: Given:If f and g are even functionthen fg is also an even function

Q: Suppose g is an odd function and let h − f o g. Is h always an  odd function? What if f is odd? What…

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Q: Let f be a function of x. f (x) = (x – 3)4 is an even function. - O True O False

A: Solution: The objective is to determine whether the given function is even or not

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: Prove that if f is a one-to-one odd function,then f −1 is an odd function.

A: A function is a relation which maps each element in its domain to exactly one value in its range. A…

Q: Find and classify the discontinuities of the following function as removable or nonremovable. If a…

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Q: If f(x) is a function that is defined for all x E R, then f (ƒ-'(x)) = = x. True False

A: A function f-1(x)  is said to be inverse of a function f(x) if the function reverses the function.…

Q: Suppose that the functions g and h are defined as follows.  g (x) = −x4  h (x) = −x3+x6 (a) Find…

A: Given, gx=-x4hx=-x3+x6

Q: Sketch a possible graph of a function that satisfies all of the following conditions: f'(2) = 0,…

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Q: (c) Show that if f is entire and |2020 + if(z)| 2020 for all z, then f is a constant function.

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Q: Given that the domain of a one-to-one function f is [−3, 5) and the range of f is (−2, ∞), state the…

A: Given,

Q: Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.

A: Given that f(x) and g(x) are both even functions.  That means: f(-x)=f(x) and g(-x)=g(x) [by…

Q: Consider these functions from the set of students in a discrete mathematics class. Under what…

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

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Q: Sketch the graph of a function that satisfies all of the given conditions. f'(0) f'(x) > 0 if x 4,…

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Q: If the following arrow diagram defines a function f, then the pre-image of 4 is A B f. A +B 1 3 9 4…

A: Given ,  This arrow diagram defines a function f , then  We have to find the pre - image of 4

Q: Find and classify the discontinuities of the following function as removable or nonremovable. If a…

A: The given function is: h(x)=x2-16x-4

Q: Suppose g is an even function and let h = f ° g . Is h alwaysan even function?

A: Suppose g is an even function and let h = f ° g . Our aim is to tell whether h is always an even…

Q: Find the domain of the below function: g(x)=In(x-x²)

A: For a function, y=f(x), the set of real values of x for which f(x) is defined is called the domain…

Q: If f(x) is a function that is defined for all x E R, then f(ƒ-'(x)) = = x. True

A: Let,  f(x) = a*x+b f-1(x) = (x-b)/a

Q: Find the domains of defination of each of the following function: Vlog.x-2 0/(x)-

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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: Suppose f is a one-to one function with domain A and range B, then the domain of the function f1 is…

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Q: Suppose that the function f is defined as follows. -2 if -3.5<xs-2.5 -1 if-2.5<xs-1.5 f(x) =(0 if…

A: Given function is, f(x)=-2  ;-3.5&lt;x≤-2.5-1  ;-2.5&lt;x≤-1.50     ;-1.5&lt;x&lt;-0.51…

Q: . Suppose g is an even function and let h=fog . Is h alwaysan even function?

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Q: f (x) = x³ + 4x² + 4x + 2

A: fx=x3+4x2+4x+2 Now let c be any real number. Then, fc=c3+4c2+4c+2 &amp;…