Inverse OF A ONE-TO-ONE FUNCTIONQ22.pptx

General Mathematics

1. Inverse OF A ONE-TO-ONE FUNCTION

2. REVIEW What is one-to-one function? When given two functions, how will you verify that they are the reverse of each other and that they are one-to-one? When given

3. Which of the following graphs illustrate a one-to-one function?

4. I DON’T LOVE YOU ANYMORE I don’t love you anymore… I would be lying if I said That I still love you the way I always did. I’m sure Nothing was in vain.

5. And I feel inside of me that You mean nothing to me I could never really say that Our time together matters.

6. I feel more and more that I’m forgetting you… And I will never use the phrase I love you. I’m sorry but I must tell the truth.

7. I’M SORRY BUT I MUST TELL THE TRUTH I love you. And I will never use the phrase I’m forgetting you… I feel more and more that Our time together matters.

8. I could never really say that You mean nothing to me And I feel inside of me that Nothing was in vain.

9. I’m sure That I still love you the way I always did. I would be lying if I said I don’t love you anymore…

10. Inverse OF A ONE-TO-ONE FUNCTION

11. f(x)=2x+3 x -1 1 2 3 y

12.   x y

13.   x -1 1 2 3 y 1 3 5 7 9   x 1 3 5 7 9 y -1 1 2 3

14. PROPERTIES OF INVERSE FUNCTION is one-to-one function; is also one-to-one   2. Domain of = Range of   3. Range of = Domain of  

15. Steps in solving the inverse of a one-one-function Substitute y for f(x). Interchange x and y. Solve, if possible, for y in terms of x. Substitute for y. Verify that the domain of f is the range of and that the range of f is the domain of .  

16. EXAMPLE # 1 FIND THE DOMAIN AND RANGE OF INVERSE FUNCTION   SOLUTION: DOMAIN:   RANGE:   To find the domain and range of   DOMAIN :     RANGE :       Substitute y for f(x). Interchange x and y.   Solve y in terms of x.       Substitute for y.  

17. GROUP ACTIVITY

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