3 9 3 9 if 3 goes in 9 comes out if 3 goes in 9 also

This preview shows 3 out of 4 pages.

3 9 –3 9 If 3 goes in, 9 comes out. If –3 goes in, 9 also comes out. No problem: 9 3 9 –3 But its inverse would have to turn 9 into both 3 and –3. No function can do this, so there is no inverse. In general, any function that turns multiple inputs into the same output does not have an inverse function. What does that mean in the real world? If we can convert Fahrenheit to Celsius, we must be able to convert Celsius to Fahrenheit. If we can ask “How much money did Alice make in 3 days?” we
Image of page 3

Subscribe to view the full document.

must surely be able to ask “How long did it take Alice to make $500?” When would you have a function that cannot be inverted? Let’s go back to this example: Recall the example that was used earlier: “Max threw a ball. The height of the ball depends on how many seconds it has been in the air.” The two variables here are h (the height of the ball) and t (the number of seconds it has been in the air). The function h (t) enables us to answer questions such as “After 3 seconds, where is the ball?” The inverse question would be “At what time was the ball 10 feet in the air?” The problem with that question is it may well have two answers ! The ball is here... ...after this much time has elapsed 10 ft 2 seconds (*on the way up) 10 ft 5 seconds (*on the way back down) So what does that mean? Does it mean we can’t ask that question? Of course not. We can ask that question, and we can expect to mathematically find the answer, or answers—and we will do so in the quadratic chapter. However, it does mean that time is not a function of height because such a “function” would not be consistent: one question would produce multiple answers.
Image of page 4
You've reached the end of this preview.
  • Fall '12
  • JenniferSera
  • Inverse Functions, Continuous function, Inverse function, Alice, Function composition

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern