Understanding the equation form of a function by using examples. Click on the link to Watch the VIDEO explanation: Watch Video
Equation Form of a function
A function is a relation R from set A to set B in which each element x in set A has a unique association with an element Y in set B for all the order pass x, y belonging to R.
Consider set A is equal to 1 2 3 and set B is equal to 4 8 12 and set R is equal to 1,4 2,8 3, 12. Here is a relation R is a function from set A to Set B. The function is denoted by the single f.
f is a function of set A to set B. If the ordered pair x,y belongs to f then y is a function of x.
In other words for the element x the value of the function is y.
In this example the function is written in a roster form as 1,4 2,8 3,12 it can be written in equation form as y is equal to 4x if x is equal to 1 then y is equal to 4, if x is equal to 2 then y is equal to 8, if x is equal to 3 then y is equal to 12.
f is a function from x to 4x where x is equal to 1, 2, 3 where x belongs to a
Example 1 Given function g. x tends to 2x plus 3 where x belongs to 2, 3, 4.
Find the values of g of 2, g of 3 , g of 4
Solution:
Function g : x tend to 2x plus 3 implies g of x is equal to 2x plus 3.
Therefore, g of 2 is equal to 2 into 2 plus 3 is equal to 7
g of 3 is equal to 2 into 3 plus 3 is equal to 9
g of 4 is equal to 2 into 4 plus 3 is equal to 11
Example 2 Given f: x tends to 2x minus 3 where x belongs to -1, 0,1.
Find the values of f of -1, f of 0 , f of 1
Solution:
F : x tend to 2x minus 3
Implies f of x is equal to 2x minus 3
Therefore, f of minus1 is equal to 2 into minus 1 minus 3 i.e., equal to minus 2 minus 3 i.e., equal to minus 5
f of 0 is equal to 2 into 0 minus 3 i.e., equal to 0 minus 3 i.e., equal to minus 3
f of 1 is equal to 2 into 1 minus 3 i.e., equal to 2 minus 3 i.e., equal to minus 1.
Equation Form of a function
A function is a relation R from set A to set B in which each element x in set A has a unique association with an element Y in set B for all the order pass x, y belonging to R.
Consider set A is equal to 1 2 3 and set B is equal to 4 8 12 and set R is equal to 1,4 2,8 3, 12. Here is a relation R is a function from set A to Set B. The function is denoted by the single f.
f is a function of set A to set B. If the ordered pair x,y belongs to f then y is a function of x.
In other words for the element x the value of the function is y.
In this example the function is written in a roster form as 1,4 2,8 3,12 it can be written in equation form as y is equal to 4x if x is equal to 1 then y is equal to 4, if x is equal to 2 then y is equal to 8, if x is equal to 3 then y is equal to 12.
f is a function from x to 4x where x is equal to 1, 2, 3 where x belongs to a
Example 1 Given function g. x tends to 2x plus 3 where x belongs to 2, 3, 4.
Find the values of g of 2, g of 3 , g of 4
Solution:
Function g : x tend to 2x plus 3 implies g of x is equal to 2x plus 3.
Therefore, g of 2 is equal to 2 into 2 plus 3 is equal to 7
g of 3 is equal to 2 into 3 plus 3 is equal to 9
g of 4 is equal to 2 into 4 plus 3 is equal to 11
Example 2 Given f: x tends to 2x minus 3 where x belongs to -1, 0,1.
Find the values of f of -1, f of 0 , f of 1
Solution:
F : x tend to 2x minus 3
Implies f of x is equal to 2x minus 3
Therefore, f of minus1 is equal to 2 into minus 1 minus 3 i.e., equal to minus 2 minus 3 i.e., equal to minus 5
f of 0 is equal to 2 into 0 minus 3 i.e., equal to 0 minus 3 i.e., equal to minus 3
f of 1 is equal to 2 into 1 minus 3 i.e., equal to 2 minus 3 i.e., equal to minus 1.
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