4.* (a) Let S = {1, 2, 3, 4}. Define F: SN by F(x) = x² for each x = S. What is the range of the function F and what is F(S)? How do these two sets compare? Now let A and B be sets and let f: A B be an arbitrary function from A to B. (b) Explain why f(A) = range(f). (c) Define a function g: A f(A) by g(x) = f(x) for all x in A. Prove that the function g is a surjection.

Q: Let a E C, with la < 1. Consider the transformation oa defined for any z € C with |2| <1 by 2 - a…

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Q: Find f(a), f(a+h), and the difference quotient for the function given below.

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A: The detailed solution is as follows below:

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A: Consider the provided function, fx=xx-1 Find the formula of ffx. We can write as, ffx=f∘fx. So,…

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A: Given function is fx=3x2+x-5. (a) To find f-2. Solution: We have fx=3x2+x-5. Put x=-2…

Q: a) y = -3f(x) Domain: Submit Answer Incorrect. Tries 1/99 Previous Tries Range: Submit Answer Tries…

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Q: The function f(x) is defined as f(x) = 2x + 5. What is the value of f(- 7/4)? a. -17 b. 3/2 c. 17/2…

A: given f(x)= 2x+5 f(-7/4)= 2(-7/4)+5 =-7/2+5 = -3.5+5= 1.5 = 3/2 f(-7/4)= 3/2

Q: Which table does not represent a function of x?

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Q: Assume that the function f is a one-to-one function.  (a) If f(8) = 6, find f -1 (6) (b) If f…

A: (a) Given that f(8)=6.

Q: Let f be a function. Then f (a) + f (b) = f (a + b) . O True O False

A: We need to proveor disprove if  fa+fb=fa+b

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A: topic - composite functions

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A: Here is the solution of the given problem.

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Q: 3. Which representation shows y as a function of x? A C y 3 -5 -1 7. 3 -2 -1 7. B D ((-3,6). (-2,6),…

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A: To evaluate the given expression with the given table values.

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A: Use one to one function property

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A: Given that for f(x) Domain [-6,-2] and  Range [-10,-4]

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Q: 1a) Let A = {1, 6, 12}, B = {0, 2, 12}. The following are all relations from A to B, but which are…

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