Redefine the function () = | − | − | + |. Write its
domain also.
Answers
Answer:
What you have written not understand
Answer:
Step-by-step explanation:
We know that,
If n(A) = p and n(B) = q, then n(A × B) = pq
From the given,
n(A × A) = 9
n(A) × n(A) = 9,
n(A) = 3 ……(i)
The ordered pairs (-1, 0) and (0, 1) are two of the nine elements of A × A.
Therefore, A × A = {(a, a) : a ∈ A}
Hence, -1, 0, 1 are the elemets of A. …..(ii)
From (i) and (ii),
A = {-1, 0, 1}
The remaining elements of set A × A are (-1, -1), (-1, 1), (0, -1), (0, 0), (1, -1), (1, 0) and (1, 1).
Q.3: Express the function f: A—R.f(x) = x2 – 1. where A = { -4, 0, 1, 4) as a set of ordered pairs.
Solution:
Given,
A = {-4, 0, 1, 4}
f(x) = x2 – 1
f(-4) = (-4)2 – 1 = 16 – 1=16
f(0) = (0)2 – 1 = -1
f(1) = (1)2 – 1 = 0
f(4) = (4)2 – 1 = 16 – 1 =15
Therefore, the set of ordered pairs = {(-4, 15), (0, -1), (1, 0), (4, 15)}
hopr it helps
:)