Function rule in algebra
Introduction :
Function rule in algebra means that we have to perform the arithmetic operation of two functions. Mainly four function rule are available in algebra. Addition function rule, subtraction function rule, multiplication function rule, division function rule. These basic functions are can written like as
Basic algebra function operations:
Example problems in function rule algebra:
Example1:
f(x) = 2x + 2 and g(x) = 2x Find the function of f(x) + g(x) = ?
Solution:
Given functions are
f(x) = 2x + 2
g(x) = 2x
Here we have to use the addition rule of function
f+ g (x) = f(x) + g(x) ( add the function separately)
f(x) + g(x) = (2x + 1) + (2x)
= 2x + 2 + 2x
= 4x + 2
=2(2x+1)
Example 2:
f(x)=8x+4 and g(x)= 5x Find the function of f(x)-g(x)=?
Solution:
Given functions are
f(x) =8x+4
g(x)=5x
Here we have to use the subtraction function
`f(x)-g(x)= (8x+4)-(5x)`
`f- g(x)=8x+4-5x`
=8x-5x+4
=3x+4
Example 3:
f(x)=3x+2 and g(x)= 5x Find the function of f(x)*g(x)=?
Solution:
Given functions are:
f(x)= 3x+2
gx)=5x
here we have to use the multiplication function rule
`f(x)*g(x)=f.g(x)`
`f.g(x)= (3x+2)(5x)`
=15x2+10x(multiplication)
=5(3x2+2)(take common to the outside)
Example problems in function rule algebra:
Example 4:
f(x)=15x and g(x)= 5x Find the function of f(x)/g(x)=?
Solution:
Given functions are
f(x)=15x
g(x)= 5x
Have we have to use the division rule function
f(x)/g(x)= f/g(x)
f/g(x)= 15x/5x
=3
Example 5:
Find the range of values to the function f(x)= 3x2+2 Find f(x)=( 0,1,2,3)
Solution:
Given function is
f(x)= 3x2+2
Range of the function f(x)=( 0,1,2,3)
Here we have to substitute range of x value to the function f(x)= 3x2+2
f(x)= 3x2+2
Substitute x=0
f(0)=3(0)+2=>2
Substitute x=1
f(1)= 3x2+2
f(1)= 3(1)2+2
=3+2
f(1)=5
f(2)= 3x2+2
Substitute x= 2 to the function
f(2)= 3(2)2+2
=3(4)+2
=12+2
=14
Substitute x=3 to the function
f(3)= 3x2+2
f(3)= 3(3)2+2
=3(9)+2
=27+2
=29
Range of functions are = f(0)=2, f(1)=5, f(2)=14 , f(3)=29
Example 6:
Check whether the function is commutative or not?
Solution:
Property for commutative function
(f. g)(x)= (g. f)(x)
Here f(x)=x-3
g(x)=2x2 -1
g(f(x))=2(x-3)2-1
=2(x2—6x+9)-1
=2x2—12x+17
F(g(x))=( 2x2 -1)-3
=2x2 -4
g(f(x))=2(x-3)2-1≠ f(g(x))=( 2x2 -1)-3
So the function s are not commutative
I like to share this The Commutative Property of Addition and algebra 1 with you all through my blog.
Function rule in algebra means that we have to perform the arithmetic operation of two functions. Mainly four function rule are available in algebra. Addition function rule, subtraction function rule, multiplication function rule, division function rule. These basic functions are can written like as
Basic algebra function operations:
- (f + g)(x) = f (x)+ g (x)
- (f – g)(x) = f (x) – g (x)
- (f .g)(x) = f (x) . g (x)
- (f/g )( x)=f(x)/g(x)
Example problems in function rule algebra:
Example1:
f(x) = 2x + 2 and g(x) = 2x Find the function of f(x) + g(x) = ?
Solution:
Given functions are
f(x) = 2x + 2
g(x) = 2x
Here we have to use the addition rule of function
f+ g (x) = f(x) + g(x) ( add the function separately)
f(x) + g(x) = (2x + 1) + (2x)
= 2x + 2 + 2x
= 4x + 2
=2(2x+1)
Example 2:
f(x)=8x+4 and g(x)= 5x Find the function of f(x)-g(x)=?
Solution:
Given functions are
f(x) =8x+4
g(x)=5x
Here we have to use the subtraction function
`f(x)-g(x)= (8x+4)-(5x)`
`f- g(x)=8x+4-5x`
=8x-5x+4
=3x+4
Example 3:
f(x)=3x+2 and g(x)= 5x Find the function of f(x)*g(x)=?
Solution:
Given functions are:
f(x)= 3x+2
gx)=5x
here we have to use the multiplication function rule
`f(x)*g(x)=f.g(x)`
`f.g(x)= (3x+2)(5x)`
=15x2+10x(multiplication)
=5(3x2+2)(take common to the outside)
Example problems in function rule algebra:
Example 4:
f(x)=15x and g(x)= 5x Find the function of f(x)/g(x)=?
Solution:
Given functions are
f(x)=15x
g(x)= 5x
Have we have to use the division rule function
f(x)/g(x)= f/g(x)
f/g(x)= 15x/5x
=3
Example 5:
Find the range of values to the function f(x)= 3x2+2 Find f(x)=( 0,1,2,3)
Solution:
Given function is
f(x)= 3x2+2
Range of the function f(x)=( 0,1,2,3)
Here we have to substitute range of x value to the function f(x)= 3x2+2
f(x)= 3x2+2
Substitute x=0
f(0)=3(0)+2=>2
Substitute x=1
f(1)= 3x2+2
f(1)= 3(1)2+2
=3+2
f(1)=5
f(2)= 3x2+2
Substitute x= 2 to the function
f(2)= 3(2)2+2
=3(4)+2
=12+2
=14
Substitute x=3 to the function
f(3)= 3x2+2
f(3)= 3(3)2+2
=3(9)+2
=27+2
=29
Range of functions are = f(0)=2, f(1)=5, f(2)=14 , f(3)=29
Example 6:
Check whether the function is commutative or not?
Solution:
Property for commutative function
(f. g)(x)= (g. f)(x)
Here f(x)=x-3
g(x)=2x2 -1
g(f(x))=2(x-3)2-1
=2(x2—6x+9)-1
=2x2—12x+17
F(g(x))=( 2x2 -1)-3
=2x2 -4
g(f(x))=2(x-3)2-1≠ f(g(x))=( 2x2 -1)-3
So the function s are not commutative
I like to share this The Commutative Property of Addition and algebra 1 with you all through my blog.