Exercise 6: Sets A and X are defined as: A = { a, b, c, d } X = { 1, 2, 3, 4 } A

Question

Exercise 6:
Sets A and X are defined as:
A = { a, b, c, d }
X = { 1, 2, 3, 4 }
A function f: A X is defined to be
f = { (a, 3), (b, 1), (c, 4), (d, 1) }
a. What is the target (or co-domain) of function f?

b. What is the range of function f?

c. What is f(c)?

d. What is the domain of function f?

Exercise 8: For each of the following functions, indicate whether the function has a well-defined inverse. If the inverse is well-defined, give the input/output relationship of f-1.

a. f: Z Z. f(x) = 2x + 3

b. f: R R. f(x) = 2x + 3

Explanation / Answer

Given A = { a, b, c, d }
X = { 1, 2, 3, 4 }
A function f: A X is defined to be
f = { (a, 3), (b, 1), (c, 4), (d, 1) }
a. What is the target (or co-domain) of function f?

The set X is co domain{1,2,3,4}
b. What is the range of function f?

The outcomes of function is range I.e the values of y

{3,1,4}
c. What is f(c)?
f(c)=4
d. What is the domain of function f?

{a,b,c,d}

Exercise 8:

a. f: Z Z. f(x) = 2x + 3 inverse is available.

Inverse of f is( x-3)/2

Relation between f and f inverse:

f(2)=7; f-1(7)=2;

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