Advertisements
Advertisements
प्रश्न
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{x - 7}\]
उत्तर
(ii) Given:
Domain of f :
Clearly, f (x) is not defined for all (x -7) = 0 i.e.x = 7.
At x = 7, f (x) takes the intermediate form \[\frac{1}{0} .\]
Hence, domain ( f ) = R - { 7 }.
APPEARS IN
संबंधित प्रश्न
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B).
If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.
If A = {–1, 1}, find A × A × A.
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C)
If A = {1, 2} and B = {1, 3}, find A × B and B × A.
If A and B are two set having 3 elements in common. If n(A) = 5, n(B) = 4, find n(A × B) and n[(A × B) ∩ (B × A)].
Let A and B be two sets. Show that the sets A × B and B × A have elements in common iff the sets A and B have an elements in common.
State whether of the statement is true or false. If the statement is false, re-write the given statement correctly:
If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}
Given A = {1, 2, 3}, B = {3, 4}, C ={4, 5, 6}, find (A × B) ∩ (B × C ).
If A = {2, 3}, B = {4, 5}, C ={5, 6}, find A × (B ∪ C), A × (B ∩ C), (A × B) ∪ (A × C).
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:
(i) A × (B ∪ C) = (A × B) ∪ (A × C)
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:
(ii) A × (B ∩ C) = (A × B) ∩ (A × C)
If A = {1, 2, 3}, B = {4}, C = {5}, then verify that:
(iii) A × (B − C) = (A × B) − (A × C)
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:
(i) A × C ⊂ B × D
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(i) A × (B ∩ C)
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(ii) (A × B) ∩ (A × C)
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(iii) A × (B ∪ C)
Prove that:
(i) (A ∪ B) × C = (A × C) ∪ (B × C)
(ii) (A ∩ B) × C = (A × C) ∩ (B×C)
Find the domain of the real valued function of real variable:
(iii) \[f\left( x \right) = \frac{3x - 2}{x + 1}\]
Find the domain of the real valued function of real variable:
(iv) \[f\left( x \right) = \frac{2x + 1}{x^2 - 9}\]
Find the domain of the real valued function of real variable:
(i) \[f\left( x \right) = \sqrt{x - 2}\]
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{\sqrt{x^2 - 1}}\]
Find the domain of the real valued function of real variable:
(iv) \[f\left( x \right) = \frac{\sqrt{x - 2}}{3 - x}\]
Find the domain and range of the real valued function:
(ii) \[f\left( x \right) = \frac{ax - b}{cx - d}\]
Find the domain and range of the real valued function:
(vii) \[f\left( x \right) = - \left| x \right|\]
Find the domain and range of the real valued function:
(ix) \[f\left( x \right) = \frac{1}{\sqrt{16 - x^2}}\]
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine A × B
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine is A × B = B × A?
If A = {2, 4, 6, 9} and B = {4, 6, 18, 27, 54}, a ∈ A, b ∈ B, find the set of ordered pairs such that 'a' is factor of 'b' and a < b.
Let A = {–1, 2, 3} and B = {1, 3}. Determine A × B
Let A = {–1, 2, 3} and B = {1, 3}. Determine B × A
Let A = {–1, 2, 3} and B = {1, 3}. Determine B × B
If P = {x : x < 3, x ∈ N}, Q = {x : x ≤ 2, x ∈ W}. Find (P ∪ Q) × (P ∩ Q), where W is the set of whole numbers.
A = {x : x ∈ W, x < 2} B = {x : x ∈ N, 1 < x < 5} C = {3, 5} find A × (B ∩ C)
