Advertisements
Advertisements
प्रश्न
Find the domain of the real valued function of real variable:
(i) \[f\left( x \right) = \sqrt{x - 2}\]
उत्तर
(i) Given:
⇒ x ∈ [2, ∞)
Hence, domain (f) = [2, ∞) .
APPEARS IN
संबंधित प्रश्न
State whether the following statement is true or false. If the statement is false, rewrite the given statement correctly.
If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B.
State whether the following statement is true or false. If the statement is false, rewrite the given statement correctly.
If A = {1, 2}, B = {3, 4}, then A × (B ∩ Φ) = Φ.
If A = {–1, 1}, find A × A × A.
If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.
If A = {1, 2, 3} and B = {2, 4}, what are A × B, B × A, A × A, B × B and (A × B) ∩ (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.
Let A = {1, 2, 3, 4} and R = {(a, b) : a ∈ A, b ∈ A, a divides b}. Write R explicitly.
State whether of the statement is true or false. If the statement is false, re-write the given statement correctly:
(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ ϕ) = ϕ.
If A = {1, 2}, from the set A × A × A.
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:
(ii) A × (B ∩ C) = (A × B) ∩ (A × C)
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)
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
(iv) (A × B) ∪ (A × C)
Prove that:
(i) (A ∪ B) × C = (A × C) ∪ (B × C)
(ii) (A ∩ B) × C = (A × C) ∩ (B×C)
If A × B ⊆ C × D and A × B ≠ ϕ, prove that A ⊆ C and B ⊆ D.
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{x - 7}\]
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:
(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:
(i) \[f\left( x \right) = \frac{ax + b}{bx - a}\]
Find the domain and range of the real valued function:
(v) \[f\left( x \right) = \frac{x - 2}{2 - x}\]
Find the domain and range of the real valued function:
(vi) \[f\left( x \right) = \left| x - 1 \right|\]
Find the domain and range of the real valued function:
(vii) \[f\left( x \right) = - \left| x \right|\]
Find f + g, f − g, cf (c ∈ R, c ≠ 0), fg, \[\frac{1}{f}\text{ and } \frac{f}{g}\] in :
(a) If f(x) = x3 + 1 and g(x) = x + 1
Let f(x) = 2x + 5 and g(x) = x2 + x. Describe (i) f + g (ii) f − g (iii) fg (iv) f/g. Find the domain in each case.
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 B × A
Let A = {1, 2, 3, 4} and B = {5, 7, 9}. Determine is A × B = B × A?
Let A = {–1, 2, 3} and B = {1, 3}. Determine B × B
A = {x : x ∈ W, x < 2} B = {x : x ∈ N, 1 < x < 5} C = {3, 5} find A × (B ∩ C)
State True or False for the following statement.
If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, then (A × B) ∪ (A × C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}.
State True or False for the following statement.
If A × B = {(a, x), (a, y), (b, x), (b, y)}, then A = {a, b}, B = {x, y}
The number of elements in the set {x ∈ R: (|x| –3)|x + 4| = 6} is equal to ______.
