हिंदी

Find the Domain of the Real Valued Function of Real Variable: (Iii) F ( X ) = 3 X − 2 X + 1 - Mathematics

Advertisements
Advertisements

प्रश्न

Find the domain of the real valued function of real variable: 

(iii) \[f\left( x \right) = \frac{3x - 2}{x + 1}\]

 

उत्तर

(iii) Given:

\[f\left( x \right) = \frac{3x - 2}{\left( x + 1 \right)}\]
Domain of f :
Clearly,  (x) is not defined for all (x + 1)  = 0, i.e. x = - 1.
At x = -1,  f (x) takes the intermediate form \[\frac{1}{0} .\]
Hence, domain ( f ) = R - { - 1 }.

 

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Functions - Exercise 3.3 [पृष्ठ १८]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 3 Functions
Exercise 3.3 | Q 1.3 | पृष्ठ १८

वीडियो ट्यूटोरियलVIEW ALL [1]

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.


State whether the following statement is true or false. If the statement is false, rewrite the given statement correctly.

If P = {m, n} and Q = {n, m}, then P × Q = {(m, n), (n, m)}.


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.


Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that   A × C is a subset of B × D


Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.


If A = {1, 2, 3} and B = {2, 4}, what are A × BB × AA × AB × B and (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 = {(ab) : a ∈ Ab ∈ Aa 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 = {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

(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: 

(iv)  \[f\left( x \right) = \frac{2x + 1}{x^2 - 9}\]

 


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:

(iv) \[f\left( x \right) = \sqrt{x - 3}\]

 


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:

(vii)  \[f\left( x \right) = - \left| x \right|\]

 


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 n (A × B) = n (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 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)


State True or False for the following statement.

If P = {1, 2}, then P × P × P = {(1, 1, 1), (2, 2, 2), (1, 2, 2), (2, 1, 1)}


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)}.


The number of elements in the set {x ∈ R: (|x| –3)|x + 4| = 6} is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×