One-one function
Every one element of A corresponds to one element of B. Every first element has a corresponding second element. One-one relations in examples 1 and 2 are called one-one functions. Every element of set A has one image in set B. {(1h..
Every one element of A corresponds to one element of B. Every first element has a corresponding second element. One-one relations in examples 1 and 2 are called one-one functions. Every element of set A has one image in set B. {(1h..Linear Equations in One Variable
Linear Equations in One Variable - An equation of one variable and of first order (i.e., its highest power is one) is called a Linear equation. Such an equation has only one solution. A solution is also called the 'root' of the given equation.An equ..
Linear Equations in One Variable - An equation of one variable and of first order (i.e., its highest power is one) is called a Linear equation. Such an equation has only one solution. A solution is also called the 'root' of the given equation.An equ..Suggested answer:
2x + y = 5 y = 5 - 2x Put x = 0, y = 5 x = 1, y = 5 - 2 = 3 x = 2, y = 5 - 4 = 1 x = 3, y = 5 - 6 = -1..
Relation
A x B = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 3), (3, 5)} (i) = {(3, 3)} is the only pair which satisfies the relation x = y. R 'is equal to' is a subset of A x B. (ii) S = {(x, y)..
A x B = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 3), (3, 5)} (i) = {(3, 3)} is the only pair which satisfies the relation x = y. R 'is equal to' is a subset of A x B. (ii) S = {(x, y)..Problems on Simultaneous Equations
Solve the following Systems of linear equations : 1. If one number is thrice the other and their sum is 60, find the numbers. 2. Find the fraction which becomes 1/2 when the denominator is increased by 5 and is equal to 1/3 when the numerat..
Function Solved Examples
Function Solved Examples - The arrow diagram represents a relation from set A to set B. (i) Represent the relation in roster form. (ii) Is this relation a function? Give reason for your answer. (i) {(1, 2), (2, 4), (5, 2), (3, 10), (4, 10)} (ii) Yes it is a f..
Question 8
Question: Solve the following equation: Answer: 2x-(1-2x) = 5-3(1+x) 2x-1+2x = 5-3-3x 4x+3x = 5-3+1 7x=3 ..
Question: Solve the following equation: Answer: 2x-(1-2x) = 5-3(1+x) 2x-1+2x = 5-3-3x 4x+3x = 5-3+1 7x=3 ..Identical equations or Identities
Now study the equations given below: a) x + 3 + x + 4 = 2x + 7 2x + 7 = 2x + 7 (By simplification) [ \ any value given to 'x' always satisfies the equation] Similarly, b) (3a + 4) + 2 (a - 1) = 5a + 2 i.e., 5a + 2 = 5a + 2 (By simplificati..
Example:
Find at least 3 sets of values for the variables satisfying the equation. 2x+y=5 Express y in terms of x. y=5-2x Select three values of x, find corresponding values of y. x=0, y=5-(2x0)=5 x=1, y=5-(2x1)=3 x=-1..
Find at least 3 sets of values for the variables satisfying the equation. 2x+y=5 Express y in terms of x. y=5-2x Select three values of x, find corresponding values of y. x=0, y=5-(2x0)=5 x=1, y=5-(2x1)=3 x=-1..Ordered Pairs, Equivalence relation
Ordered Pairs - An ordered pair has a pair of elements which occur in a definite order.An ordered pair has a pair of elements which occur in a definite order. Take two numbers 3 and 5. If they form a pair (3,5) and the order of the numbers cannot be changed, ..
Ordered Pairs - An ordered pair has a pair of elements which occur in a definite order.An ordered pair has a pair of elements which occur in a definite order. Take two numbers 3 and 5. If they form a pair (3,5) and the order of the numbers cannot be changed, .. Result
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