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: What value of x makes the relation {(1,5), (x, 8), (-7,9)} a function?

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Q: If f(x) = x2, what is the ordered pair for x = 7 ? %3D O (7,21) O (7,49) O (7,9) O (7,14)

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Q: (a) Suppose f:R³ → R² is a function for which and Could f be linear? Why or why not? (b) . that…

A: Part (a):   A function f: R3 to R2 is linear:   By the definition of linear function maps zero…

Q: Refer to the function f = {(-2, 4), (9, 6), (2, 7), (7, 9)}. Determine f(-2). f(-2)=1 X

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Q: How many fixed points are there for the function f(x)=x3

A: FInd How many fixed points are there for the function f(x)=x3.Fixed point of a function are point…

Q: A function f is defined by Ax + 5 f(x) 6x - 2 If f(1) = 4, find A.

A: Given: fx=Ax+56x-2  ……1   and, f1=4  ……2   To find: A

Q: Refer to the functions f and g and evaluate the functions at x= -4 f={(6,8), (4,5), (-4,-4), (0,0),…

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Q: 1) Let f(x) be a function with Domain [-6,-2] and  Range [-10,-4]. Find the domain and range of the…

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

Q: Let f(x) be the function f(x) 1. Find the following: x + 1 f(11) = f( – 10) | (4) 2 (-) f |

A: Given function is fx=xx+1-1. Put x=11 in the function. f11=1111+1-1=1112-1=-112 Therefore, f11=-112.

Q: Given that A = {1, 2, 3, 4, 5} and B = {x, y, z}, determine which of the sets of ordered pairs…

A: 1.  i) This ordered pair doesn't represents a function because the values 'y' corresponding to x= 4…

Q: Let f = {(- 2,1),(1, - 1)} and g = {(-2, - 4),(3,0),(5,6)}. Find f+g and its domain.

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Q: Make a table of values for f(x) = x² - 4 showing function values for x = 4, 6, 8,.... f(x) x 4 6 8…

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