4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that {f(x) EYE A}, and f-¹(A) = {xe A: f(x) = A}. f(A) 1 (a) Show that A CS-¹(f(A)). (b) Give an example of a function f : X → Y and the set A such that f(f(A)) # A.

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

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A: a)

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Q: 4. A function f may have the property that, for all numbers a and b in the domain of f, f(a) + f(b)…

A: GIVEN : f(a) + f(b) = f(a + b)

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

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Q: a) Use the graph to list in order, from smallest to largest. 2- -1 -0.5 9 0.5 1 15 2 25 3 3.5 b)…

A: From the graph the integral can be find by adding area under curves. If the area is  under curve is…

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

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A: Given the graph of f. The objective is to draw the graph of f-1 and to find the values of f-1(2) and…

Q: 12. Let f be the function f(x)={ x² - 3bx+2; x2 For what value of b is f continuous at x = 2 ? (A) 0…

A: To find For what values of b is f is continuous at x=2.

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: Suppose that f(x) is a continuous function with f( – 1) = - 8 and f(3) = 8. Determine which choice…

A: Always true

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: Suppose that F(x) is a function such that F"(x) = f(x). Which of the following statements is true? […

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Q: 58. Show that if f is a function and z = x+h, then f(2) – f(x) _ f(x+ h) – f(x) Z - x h

A: This question is taken from the function in which we have to prove the given equation. We can write…

Q: Let f(x) a) f(a) = g(a) = 3x + 1. and g(x) = 2x. Determine values for a such that b) f(a²) = g(2a)

A: Given: fx=3x+1 and gx=2-x. We have to determine the value for a such that a fa=ga, b fa2=g2a.

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Q: (b) Determine the range of f, if f :D → R, where f (x) = x?. I. D = (-2, 2) II. D = [-7, 2] III. D =…

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Q: A TUN f: {1,2,3,4} is defined by f(1) = 6, ƒ(2) = 7, f(3) = 8, Drag the answers into the right place…

A: Given function is f:1, 2, 3, 4 → 5, 6, 7, 8 defined by f(1) = 6, f(2) = 7, f(3) = 8, f(4) = 6

Q: Compute f(5) (e) forthe function f(x) = x³.In(x+)

A: f(x)=x3.ln(x4)f(x)=4x3ln(x)Differentiatef'(x)=4x2+3x2ln(x)f'(x)=4x2+12x2ln(x)Differentiatef''(x)=8x+…

Q: Suppose that f(x) is a function with f(5) = - 8 and f(9) = 8. Determine which choice best describes…

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