BINARY-OPERATION and OPERATION OF FUNCTION.pptx

BINARY-OPERATION

1. BINARY OPERATION JOHN CLIFFORD T. MORENO, LPT

2. A binary operation *in a set S is a way of assigning every ordered pair of elements, a and b , from the set, a unique response called c , where c is also from the set S. a * b = c First element from the set operation Second element from the set Unique response from the set

3. Binary operations include addition, subtraction, multiplication and division. The value of f(x) is obtained upon assigning a specific value for x. The variable x represents the independent variable and y represents the dependent variable.

4. Given y=f(x) and let a be in the domain of f . Then f(a) represents the second element in the pair of defining f, or the value of the function at x = a. The value of f(a) is obtained by replacing x by a in f(x).

5. Let f(x) = 2x³ - 3x² - 5 x + 2. Find: a. f(1) b. (-1) c. f(-3)

6. Solutions: a. f (1) = 2(1)³-3(1)²-5(1)+2 = -4 b. f (-1) = 2(-1)³-3(-1)²-5(-1)+2 = 2 c. f (-3) = 2(-3)³-3(-3)²-5(-3) +2 = -64

7. 2. Let f(x) = Find: a. f(2) b. f c. f(b )  

8. Solution: a. (2) = b. f c. f(b) =  

9. 3. Compute: if f(x) = 2x – 1, h Solution: = =  

10. A binary operation on a set is a calculation involving two elements of the set to produce another element of the set. Given two functions : f(x) and g(x), then Sum of two functions : f(x) + g(x) Difference of two functions : f(x) – g(x) Product of two functions : f(x) Quotient of two functions : f(x)/g(x), g(x)  

11. Operations with Functions We can add, subtract, multiply and divide functions! The result is a new function.

12. Example: Given f(x) = x² + 1 and g(x) = x² - x a. f(x) + g(x) b. f(x) – g(x) c. f(x) g(x) d.  

13. Solution: f(x)+g(x)=(x²+1)+(x²-x) = x²+1+x²-x = 2x²-x+1 f(x)-g(x) =(x²+1)-(x²-x) = x²+1-x²+x = x+1 f(x) g(x) = (x²+1)(x²-x) =  

14. Addition of Function We can add two functions: ( f+g )(x) = f(x) + g(x)   Note: we put the f+g inside () to show they both work on x.

15. Example 1 Let f(x) = 2x+3 and g(x) = x2 Find ( f+g )(x) Solution: ( f+g )(x) = f(x) + g(x) = (2x+3) + (x2) = x2+2x+3

16. Example 2 Let v(x) = 5x+1 and w(x) = 3x-2 Find ( v+w )(x) Solution: ( v+w )(x) = v(x)+w(x) =(5x+1) + (3x-2) = 8x-1

17. Subtaction of Function We can subtract two functions: (f-g)(x) = f(x) - g(x) Note:  The difference f-g is a function whose domains are the set of all real numbers common to the domain of f and g.

18. Example 3 let  f(x) = x 2 - 5 and g(x) = 5x -4 Find (f-g)(x) Solution:              (f-g)(x) = f(x)-g(x)                              =( x 2 - 5) - (5x-4)                              =x 2 - 5 - 5x +4                               =x 2 - 5x - 1

19. Multiplication of Function We can multiply two functions: ( f • g )(x) = f(x) • g(x) Note:  The product f•g is a function whose domains are the set of all real numbers common to the domain of f and g.

20. Example 4 Let  f(x) = 3x - 2 and g(x) = x 2 - 2x - 3 Find ( f • g )(x) Solution:              ( f • g )(x) = f(x) • g(x)                              =(3x - 2) (x 2 - 2x - 3)                               =3x(x 2 - 2x - 3) - 2(x 2 - 2x - 3)                               = 3x 3 - 6x 2 - 9x - 2x 2 +4x + 6                               =3x 3 -8x 2 -5x +6

21. Division of Function We can divide two functions: ( f/g)(x) = f(x) / g(x) Note:  The quotient f/g is a function whose domains are the set of all real numbers common to the domain of f and g. Where g(x) or denomenator ≠ 0.

22. Example 5 Let  f(x) = x + 3 and g(x) = x 2 + x - 9 Find (f/g)(x) Solution :                

23. ACTIVITY 3! Q: Sir kanus -a ipass ? A: I-pass ni siya dungan sa midterm napod nga activities

24. Directions: Perform the given operation. f(x) =2x – 5, g(x) = 3x – 4 a. f(x) + g(x) b. f(x) – g(x) c. f(x) g(x) d. f(x)/g(x)   f(x )=x²-4, g(x) =x+2 a. f(x) + g(x) b. f(x) – g(x) c. f(x) g(x) d. f(x)/g(x)