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Let B = {1, 2, 3, 4, 5, .....30}, A = {2...

Let B = {1, 2, 3, 4, 5, .....30}, A = {2,3, 4, 5, 6, 7, 8, 9, 10}. A relation is defined from A to B defined by R ={(a, b) : b = 4a, `a in A, b in B`}, then domain and range

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To solve the problem, we need to find the domain and range of the relation \( R \) defined from set \( A \) to set \( B \) by the rule \( R = \{(a, b) : b = 4a, a \in A, b \in B\} \). ### Step-by-Step Solution: 1. **Identify the Sets**: - Set \( A = \{2, 3, 4, 5, 6, 7, 8, 9, 10\} \) - Set \( B = \{1, 2, 3, \ldots, 30\} \) 2. **Define the Relation**: - The relation \( R \) is defined as \( R = \{(a, b) : b = 4a\} \) where \( a \in A \) and \( b \in B \). 3. **Calculate Possible Values of \( b \)**: - We will calculate \( b \) for each \( a \) in set \( A \): - For \( a = 2 \): \( b = 4 \times 2 = 8 \) - For \( a = 3 \): \( b = 4 \times 3 = 12 \) - For \( a = 4 \): \( b = 4 \times 4 = 16 \) - For \( a = 5 \): \( b = 4 \times 5 = 20 \) - For \( a = 6 \): \( b = 4 \times 6 = 24 \) - For \( a = 7 \): \( b = 4 \times 7 = 28 \) - For \( a = 8 \): \( b = 4 \times 8 = 32 \) (not in set \( B \)) - For \( a = 9 \): \( b = 4 \times 9 = 36 \) (not in set \( B \)) - For \( a = 10 \): \( b = 4 \times 10 = 40 \) (not in set \( B \)) 4. **Filter Valid Pairs**: - The valid pairs where \( b \) belongs to set \( B \) are: - \( (2, 8) \) - \( (3, 12) \) - \( (4, 16) \) - \( (5, 20) \) - \( (6, 24) \) - \( (7, 28) \) 5. **Determine the Domain**: - The domain consists of all values of \( a \) that produced valid \( b \) values: - Domain: \( \{2, 3, 4, 5, 6, 7\} \) 6. **Determine the Range**: - The range consists of all valid \( b \) values obtained from the domain: - Range: \( \{8, 12, 16, 20, 24, 28\} \) ### Final Answer: - **Domain**: \( \{2, 3, 4, 5, 6, 7\} \) - **Range**: \( \{8, 12, 16, 20, 24, 28\} \)
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AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Assignment (Section - B) Objective Type Questions (one option is correct)
  1. The domain of f(x) = (log(2)(x+4))/(x^(2) + 3x + 2) is

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  2. Let B = {1, 2, 3, 4, 5, .....30}, A = {2,3, 4, 5, 6, 7, 8, 9, 10}. A r...

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  3. Let A and B are two sets such that A xx B consists of 6 elements. If t...

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  4. Let A ={1,2,3,4,5,6} . Define a relation R from A to A by R = {(...

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  5. Let A = {2, 3, 4}, B ={3, 4, 5} be two sets and a relation R is define...

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  6. Let f(x^(3)) = x^(4) + x^(5) + x + 1, then the value of f(8) is

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  7. If f(x) = (x-1)/(x+1) then f(ax) in term of f(x) is equal to

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  8. If f(x + y, x-y) = xy then the arithmetic mean of f(x, y) and f(y, x) ...

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  9. If 2f(x^2)+3f(1/x^2)=x^2-1, then f(x^2) is

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  10. The maximum number of values of x satisfying |x-2| + |x-4| = 2 is

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  11. The value of x if 0 le |2x + 3| le 3 belongs to

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  12. If |x + 4| + |x-4|=2|x| and |x+1|+|5-x|=6 then x belongs to

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  13. If [] and {} represents the greatest integer function and fractional f...

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  14. If f(x) = cos [pi]x + cos [pi x], where [y] is the greatest integer fu...

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  15. Range of function (1)/(3- sin 3x) is

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  16. If -1 le [2x^2 -3] lt 2, then x belongs to

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  17. Range of f(x) = (x+2)/(|x+2|)

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  18. If f(x) = log ((1+x)/(1-x)), then f((2x)/(1+x^(2))) is equal to

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  19. The domain of f(x) = log |x| + 1/sqrt|x| + 1/log|x| is R - A where A i...

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  20. The largest set of real values of x for which f(x)=sqrt((x + 2)(5-x))...

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