{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ch.10 Compositions, Inverses, and Combinations of Functions

# ch.10 Compositions, Inverses, and Combinations of Functions...

This preview shows pages 1–8. Sign up to view the full content.

Chapter 10 Compositions, Inverses, and Combinations of Functions 10.1 Composition of Functions

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

View Full Document
Key Points Finding the composition of two functions numerically, graphically and symbolically Interpreting the composition of two functions Decomposing a function
Formulas for Composite Functions Example 1 Let p ( x ) = cos x + 1 and q ( x ) = x 2 + 2. a. Find a formula in terms of x for r ( x ) = p ( q ( x )). b. Find a formula s ( x ) = p(q(q(x )). c. Find a formula t ( x ) = q ( p ( x )). Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally

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

View Full Document
Decomposition of Functions Example 4 Let h ( x ) = f ( g ( x )) = . Find possible formulas for f ( x ) and g ( x ). Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally 1 2 + x e
22,36,52,54

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

View Full Document
Composition of Functions The function f ( g ( t )) is said to be a composition of f with g . The function f ( g ( t )) is defined by using the output of the function g as the input to f . The function f ( g ( t )) is only defined for values in the domain of g whose g ( t ) values are in the domain of f . The function f ( g ( t )) is said to be a composition of f with g . The function f ( g ( t )) is defined by using the output of the function g as the input to f . The function f ( g ( t )) is only defined for values in the domain of g whose g ( t ) values are in the domain of f . Functions Modeling Change: A Preparation for Calculus, 4th Edition, 2011, Connally
Chapter 10 Compositions, Inverses, and Combinations of Functions 10.2 Invertibility and Properties of Inverse Functions

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

View Full Document
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