(1) Prove that a function is simple if and only if its range {f(x) :x € X} is a finite set.

Q: Find the global maximum and minimum of the function on the given interval:f(x)=x+2x,x∈[0.5,2].

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Q: None of these such a function does not exist

A: I can be written in terms of exponential

Q: (a) Find the global maximum and minimum values of the function on the closed interval [0, 3]. f(x) =…

A: the given function  f(x) = 2x3 -3x2 -12x +15 over the interval [0, 3]

Q: Prove that f(x) = (x – 1)2 + (x + 1)? is an even function. A function k(x) is an even function if…

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Q: (a) Any critical point of a function f is either a local maximum or local minimum for f. True False

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Q: Determine the absolute maximum and minimum values of f(x) = x²e on x = [-5, 1].

A: Given: fx=x2ex on x∈-5, 1 To find the absolute maximum and absolute minimum of the given function on…

Q: Draw a function f(x), defined for all real numbers x, with one local maximum and two local minimum.

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Q: Find the absolute maximum and absolute minimum values of f on the.given interval. (2) f(x)= x+1…

A: Hi there, at a time we can answer only one question and the exact one was not specified. So, I have…

Q: Find (algebraically) the absolute maximum and minimum values of f(x) = (x^2) / (x - 1) on (1, 4), if…

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Q: 2. (a) Suppose f is a function with domain a, b). Iff is an odd function, what can be deduced about…

A: (a) We know that , if f is an odd function then    f(-x) = -f(x)  Here given that f is a function…

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: sketch the graph of a function f satisfying all of the given conditions. (i) f' (x) > 0 for all…

A: The graph of a function f satisfying all of the given conditions. (i) f' (x) > 0 for all x,…

Q: Find the absolute maximum and absolute minimum values of f on the.given interval. (4) f(x)= -3,31…

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Q: 7) Construct a table of values for the function f(x) = x 1 in the restricted domain (0, 0.5, 1, 1.5,…

A: Or

Q: Find the global maximum and minimum of the function on the given interval:f(x)=x|x−2|,x∈[0,3].

A: If x<2 then |x-2| = -(x-2)=2-x If x≥2 then |x-2|=x-2

Q: 7 Find the most general function F such that F'(): - 5V?.

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Q: Sketch the graph of a function that satisfies all of the given conditions. f'(x) > 0 for all x # 1,…

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Q: d) Let XCR be a set and f: X→ X be a function. If X is compact and convex, then f admits a fixed…

A: d) If X is compact subset of R then X is closed and bounded. If X  is convex subset of R then X is…

Q: 6. Sketch a graph of some function f(x) where the interval for f(x) > O is [2,5] and [8,).

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Q: Draw graph of a function which satisfies the conditions below. f'(x) 0 on interval (5, 7) f'(x) = 0…

A: As informations are given only in domain 0 to infinity so let's draw the graph form given datas…

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: Function f:Z → Z, defined by f(n) =n- 1 is a one-to-one function. True False

A: The given statement is true .

Q: Prove that f(x) = (x – 1)2 + (x + 1)² is an even function. A function k(x) is an even function if…

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Q: If a function is even, then for every point (x , y) on the graph of there exists another point on…

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Q: Let the function F(x) = x³ - 5x² + 4x Define in a range of [-2.5]. Show that Rolle's theorem is…

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

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x^3 − 3x^2…

A: Given,           f(x) = 2x3 − 3x2 − 36x + 3  and interval is [-3,4].

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: If  f is a continuous function defined for all real numbers    x and if the maximum value of f(x) is…

A: Given that the maximum value of f(x)= 5 and the minimum value of f(x)= -7 For f(x)=5, |f(x)|= 5 And…

Q: 5. Suppose that function f(x) satisfies f'(x) 0 at interval [a, b], then the graph of y = f(x) ( )…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x + 9/x,…

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Q: Let f be the function defined by f (x) = 6x. On which open intervals is ƒ decreasing? %3D -2 3 <글…

A: Given that: f(x)=x33-x22-6x

Q: A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(x) ≠ 1 for all real…

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Q: 13. Prove: If a function f is differentiable at some a in its domain, then f is also continuous at…

A: We have a property that, "Every differentiable function is continuous but every continuous function…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe−x^2/162,…

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Q: Sketch the graph of a function that satisfies all of the given conditions. f'(x) > 0 for all x + 1,…

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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

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

Q: The Min-Max Theorem states that a contimuous function defined on a closed, finite interval must have…

A: We have to find the absolute maximum or absolute minimum of the function f(x)= x2+1 in the interval…

Q: Let us define a number a to be a fixed point of a function f if a = f(a). (For example, if f (x) =…

A: We have to prove that a function has at most one fixed point if f'x≠1 Let us assume that the…

Q: Find the absolute extrema of the function on the closed interval.                       g(x) = ∣x +…

A: Consider the given function, gx=x+4 over the interval -7, 1 differentiating the above function we…

Q: Find the global maximum and minimum of the function on the given interval:f(x)=x+2/x,x∈[0.5,2].

A:

Q: Find the maximum and minimum value of the given function below on a given interval.

A: Given function  f(x) = 3+2x-x2     on -1.3  , 1

Q: Find the absolute maximum and absolute minimum values of f on the given interval. a) f(x) = 3x2 –…

A: topic- maxima and minima of a function take derivative to find critical points . As per bartleby…

Q: 1 a. Determine whether the Mean Value Theorem applies to the function f(x) =x+- on the interval…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) =  x x2…

A: We find the derivative of f(x) using the quotient rule

Q: (a) Suppose f is a function with domain [a, b]. If f is an odd function, what can be deduced about a…

A: (a) Here, f is an odd function. So, f(-x)=-f(x); all x∈[a,b]. So, if x is in the domain then -x is…

Q: Suppose that f is a function with f(2) &gt; 0 and f1(2) = 0. If f is a local minimum of f, what do…

A: It is supposed that f is a function with