ADD SUBTRACT MULTIPLY AND DIVIDE FUNCTIONS

About "Add subtract multiply and divide functions"

Add subtract multiply and divide functions :

Adding and subtraction functions is nothing but combining the like terms.

Let us see some example problems to understand how to add, subtract, multiply and divide functions.

Add subtract multiply and divide functions - Examples

Example 1 :

Use f(x) and g(x) to find f(x) + g(x):

f(x) = -x + 5 and g(x) = 3x + 2

Solution :

To find the sum of f(x) and g(x), we have to add these functions.

f(x) + g(x)  =  -x + 5 + 3x + 2

Now combine the like terms

  =  -x + 3x + 5 + 2

  = 2 x + 7

Example 2 :

What is (f - g) (x) ?

f(x) = 2 x² and g(x) = -4 x + 2

Solution :

(f - g) (x)  =  f(x) - g(x)

  =  2 x² - (-4 x + 2) 

  =  2 x² + 4 x - 2 

Hence the value of (f - g) (x) is 2 x² + 4 x - 2 

Example 3 :

If f(x) = 3 x + 2, k(x) = 5 x + 1 then evaluate f(2) x k(4)

Solution :

To find the value of f(2), we have apply 2 instead of x in the given function of f(x).

f(x) = 3 x + 2

f(2) = 3 (2) + 2 ==> 6 + 2 ==> 8

To find the value of k(4), we have apply 4 instead of x in the given function of k(x).

k(x) = 5 x + 1

k(4) = 5 (4) + 1 ==> 20 + 1 ==> 21

f(2) x k(4) = 8 x 21 ==> 168

Hence the value of f(2) x k(4) is 168.

Example 4 :

If f(x) = 4 x - 7, g(x) = 3x + 18 and h(x) = -5x + 2, find

(f + g - h) (x) 

Solution :

(f + g - h) (x) = f(x) + g(x) - h(x)

   =  4 x - 7 + 3 x + 18 - (-5 x + 2)

   =  4 x - 7 + 3 x + 18 + 5 x - 2

Combine the like terms

   =  4 x + 3 x + 5 x - 2 + 3 + 18 - 2

   =  12 x  + 19

Hence the value of (f + g - h) (x) is 12 x + 19.

Example 5 :

If f(x) = 6 x - 8, g(x) = (1/2) x and h(x) = x + 4, find

(f x g x h) (x) 

Solution :

(f x g x h) (x)  =  f(x) x g(x) x h (x)

f(x) x g(x)  =  (6 x - 8)(x/2)

  =  6 x²/2 - (8 x/2) 

f(x) x g(x)  =  3 x²- 4 x

f(x) x g(x) x h(x) = (3 x²- 4 x) (x + 4)

  =  3 x³ - 4 x² + 12 x² - 16 x

  =  3 x³ + 8 x² - 16 x

Hence the value of (f x g x h) (x) is 3 x³ + 8 x² - 16 x.

After having gone through the stuff given above, we hope that the students would have understood "Add subtract multiply and divide functions". 

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