Maths-
General
Easy
Question
Given x = {(2, 7), (3, 9), (5, 13), (0, 3)} be a function from Z to Z defined by f(x) = ax + b for some integral a and b. What are the values of a and b?
The correct answer is: a = 2 and b = 3.
We have given a function from Z to Z
Given x = {(2, 7), (3, 9), (5, 13), (0, 3)}
And also we have given that
f(x) = ax + b
We have to find the value of a and b .
First of all if the f is a function then its points will satisfy f(x) = ax + b
f(2) = 7
f(3) = 9
f(5) = 13
f(0) = 3
i) (2,7)
f(2) = a (2) + b
7 = 2a + b
ii) (3,9)
f(3) = a(3) + b
9 = 3a + b
Subtract equation (i) from (ii)
3a – 2a + b – b = 9 – 7
a = 2
Putting this value in equation (i)
7 = 2(2) + b
b = 7 – 4
b = 3
Therefore, value of a = 2 and b = 3.
We have to find the value of a and b .
First of all if the f is a function then its points will satisfy f(x) = ax + b
Subtract equation (i) from (ii)
Putting this value in equation (i)
Therefore, value of a = 2 and b = 3.
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Which of the following relations are functions? Give reasons.
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a) (a,a) ∈R , for all a ∈N
b) (a,b) ∈R implies (b,a) ∈R
c) (a,b) ∈R , (b,c) ∈R implies (a,c) ∈R
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a) (a,a) ∈R , for all a ∈N
b) (a,b) ∈R implies (b,a) ∈R
c) (a,b) ∈R , (b,c) ∈R implies (a,c) ∈R
Justify your answer in each case.
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Maths-
Draw and find the number of lines of symmetry for the given regular pentagon.
![](data:image/png;base64,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)
Draw and find the number of lines of symmetry for the given regular pentagon.
![](data:image/png;base64,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)
Maths-General
Maths-
Find the number of lines of symmetry for a regular heptagon.
Find the number of lines of symmetry for a regular heptagon.
Maths-General
Maths-
If A is a relation on a set R , then which one of the following is correct ?
If A is a relation on a set R , then which one of the following is correct ?
Maths-General
Maths-
Let A and B two sets such that n( AxB)= 6 . If three elements of AXB are ( 3,2)(7,5)(8,5), then
Let A and B two sets such that n( AxB)= 6 . If three elements of AXB are ( 3,2)(7,5)(8,5), then
Maths-General