8. A function f is defined on the set of natural numbers as
f(x) = x if 1 ≤ x <5
x + 3 if 5 < x ≤ 8
(X - 3)/2 if 8< x < 11
Write the function in roster form and also find the domain and range
of the function
Answers
The given function in roster form is {(1,1), (2,2), (3,3), (4,4), (6,9), (7,10), (8,11), (9,3)}
The domain of the function = {1, 2, 3, 4, 6, 7, 8, 9}
The range of the function = {1, 2, 3, 4, 9, 10, 11, 3}
Given:
A function f is defined on the set of natural numbers as
f(x) = x if 1 ≤ x <5
x + 3 if 5 < x ≤ 8
(x - 3)/2 if 8 < x < 11
To Find:
The function in roster form =?
The domain of the function =?
The range of the function =?
Solution:
A function f is defined on the set of natural numbers as
f(x) = x if 1 ≤ x <5
x + 3 if 5 < x ≤ 8
(x - 3)/2 if 8 < x < 11
If 1 ≤ x < 5, then f(x) = x
f(1) = 1
f(2) = 2
f(3) = 3
f(4) = 4
If 5 < x ≤ 8, then f(x) = x + 3
f(6) = 6 + 3 = 9
f(7) = 7 + 3 = 10
f(8) = 8 + 3 = 11
If 8 < x < 11, then f(x) = (x - 3)/2
f(9) = (9 - 3)/2 = 6/2 = 3
f(10) = (10 - 3)/2 = 7/2 = 3.5 - not defined as we need a natural number
The given function in roster form is {(1,1), (2,2), (3,3), (4,4), (6,9), (7,10), (8,11), (9,3)}
The domain of the function = {1, 2, 3, 4, 6, 7, 8, 9}
The range of the function = {1, 2, 3, 4, 9, 10, 11, 3}
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