INVERSE FNCTION.pptx general mathematics

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1. One to One function General Mathematics

2. ONE-TO-ONE FUNCTIONS

3. Determine whether the given relation is a function, whether it is one to one or not. 1. The relation pairing an SSS member to his or her SSS number. Answer: One-to-one function 2. The relation pairing a real number to its square. Answer: Not one to one Function

4. 3. The relation pairing an airport to its airport code. Answer: One to one function 4. The relation pairing a person to his or her citizenship Answer: Not One to one function

5. 5. The relation pairing Sim cards to cellphone numbers Answer: One to one function

6. General Mathematics Inverse Functions

7. INVERSE OF FUNCTIONS DEFINITION: is denoted by . It is defined by the equation (𝑦) = 𝑥 if and only if 𝑓(𝑥) = 𝑦 for any y in range B.  

8. Inverse of a relation The inverse of the ordered pairs ( x , y ) is the set of all ordered pairs ( y , x ). The Domain of the function is the range of the inverse and the Range of the function is the Domain of the inverse. Symbol: In other words, switch the x’s and y’s!

9. Example : {(1,2), (2, 4), (3, 6), (4, 8)} Inverse:  

10. Example: {(3,−2), (1,0), (5,7), (4,−4), (10,2)} To find the inverse of the given function, interchange the coordinates of each ordered pair. (3,−2)&→(−2,3) (1,0)&→(0,1) (5,7)&→(7,5) (4,−4)&→(−4,4) (10,2)&→(2,10)

11. TO FIND THE INVERSE OF FUNCTIONS A. Write the function in the form y = f(x) B. Interchange the x and y variables C. Solve for y in terms of x

12. Find Inverse:

13. Find Inverse:

14. Find Inverse:

15. Find Inverse:

16. f(x)=   F(x)= Y = X = 2y+3=3xy-4x 4x+3=3xy-2y 4x+3=y(3x-2) = Y= (x)=  

17. 10/23/2024 Sample Footer Text 20 BOARDWORK ACTIVITY

18. 1. f(x)= 3x+1 2. f(x)= 2x+7 3.f(x)= 3x 4.f(x)=5x+2 5.f(x)= 6.f(x)= 7.f(x)=   1. (x)= 2. (x)= 3. (x)= 4. (x)= 5. (x)= 6. (x)= 7. (x)=  

19. 1. g(x)= X – 4 2. f(x) = 3.f(x)= 4.f(x)=6x+2 5.f(x)= 6.s(x)= 5x-6 7.f(x)=7x³+2 8.f(x)=   1. (x)= X+4 2. (x)= 3. (x)= 4. (x)= 5. (x)= 6. (x)= 7. (x)= 8. (x)=  

20. 4.s(x) = 5x + 2 X – 3 2. f(x) = 2x + 7 3. g(x)=3x – 8 5. f(x) = x – 2 3x + 5 1. f(x) = 3x + 1 Find the inverse function of the ff. functions ACTIVITY

21. Assignment: Determine whether a function is one-to-one function or not 1. A relation pairing with book to its authors. 2. A relation pairing a real number to its cube. 3. A relation pairing a student to his or her School I.D. 4. A relation pairing a cellphone to its password. 5. A relation pairing a True or false to answers. Find the inverse function of the ff. functions; f(x) = 4x – 7 g(x) = 2x – 1 x + 4