mac1147_lecture18_1_c

mac1147_lecture18_1_c - L18 Composite Functions; One-to-one...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
196 L18 Composite Functions; One-to-one Functions; Inverse Functions A composite function fg D (read as “ f composed with g ”) is defined by () ( ) ( ( ) ) x f g x = D . The domain of D is the set of all real x in the domain of g for which ( ) gx is in the domain of f . Example : Show a diagram for the composite function ( ) ( ( ) ) x f g x = D Similarly we define: ( )( ) ( ( )) gfx g f x = D
Background image of page 1

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

View Full DocumentRight Arrow Icon
197 Example : Let () 5 fx x = and 2 2 gx x = . Find: (a) ( )(4) fg = D (b) ( )(9) gf = D (c) Find the composite functions and their domains ( ) gfx = D Domain:
Background image of page 2
198 () ( ) fg x = D Domain: Example : Using the tables, find ( )(2) D and ( )(1) gf D . What is the value of ( )(0) D ? x 1 0 1 x 3 0 2 fx 5 1 3 gx 15 6 0
Background image of page 3

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

View Full DocumentRight Arrow Icon
199 Example : Find functions f and g such that fgh = D if 32 4 () ( 1 ) hx x x =+ + 2 1 () x =− +
Background image of page 4
200 Example : An oil spill in the ocean assumes a circular shape with an expanding radius r given by 1 rt =+ , where t is the number of minutes after the measurements are started and r is measured in meters. (a) Find a formula that gives the area A of the circular region as a function of time t . (b) What is the area at the beginning? ( t = ) (c) What is the area 3 minutes later? ( t = )
Background image of page 5

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

View Full DocumentRight Arrow Icon
201
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

Page1 / 16

mac1147_lecture18_1_c - L18 Composite Functions; One-to-one...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online