{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# lecture5 - Lecture 5 Inverse Functions Logarithms(Chapter 1...

This preview shows pages 1–5. Sign up to view the full content.

Lecture 5: Inverse Functions, Logarithms (Chapter 1, Sec. 5) Def. A function f is called a one-to-one (1 - 1) function if ex. f ( x ) = x 2 + 1 ex. f ( x ) = x 3 6 - ? 6 - ? Horizontal Line Test A function is one-to-one if and only if any horizontal line intersects the graph of the function in at most one point. NOTE: Increasing/decreasing functions

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Inverse Functions Def. Let f be a one-to-one function with domain A and range B . Then it has a unique inverse function f ¡ 1 : B ! A which assigns to each y in B the unique x value in A given by f ¡ 1 ( y ) = x if and only if Thinking of x as the independent variable, we can also write f ¡ 1 ( x ) = y if and only if Note the following results of the deflnition: 1) If ( x; y ) is a point on the graph of f ( x ), then 2) domain and range of f ¡ 1
Inverse relationships f ¡ 1 ( f ( x ) ) = for every x in A f ( f ¡ 1 ( x ) ) = for every x in B ex. Show that f ( x ) = x 3 + 1 and g ( x ) = 3 p x ¡ 1 are inverse functions. ex. Find the inverse of f ( x ) = p x + 2. Check domain and range.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Inverse functions and graphs ex. Given the graph of f ( x ) = x 3 + 1, sketch the graph of the inverse function.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern