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.
Example 1 :
Use f(x) and g(x) to find f(x) + g(x):
f(x) = -x + 5 and g(x) = 3x + 2
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
(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)
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)
(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)
(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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