6_1_6_2_Presentation_0

# 6_1_6_2_Presentation_0 - SECTION 6.1 AND 6.2 COMPOSITE...

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

S ECTION 6.1 AND 6.2: C OMPOSITE O F UNCTIONS ; O NE TO O NE F UNCTIONS AND I NVERSE NCTIONS F UNCTIONS Math&141 Pre-Calculus I

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

View Full Document
Suppose that an oil tanker is leaking oil and we want to be able to determine the area of the circular oil patch around the ship. It is determined that the oil is leaking from the tanker in such a way that the radius of the circular oil patch around the ship is increasing at a rate of 3 feet per minute.
C OMPOSITE F UNCTION | Given two functions f and g, the composite function, denoted by f º g (f composed with g) is defined by: )(x) = f(g(x)) | (f º g)(x) f(g(x)) | So on the previous slide: | r(t) = 3t (radius of the spill is 3 feet per minute x time in minutes) | A(r) = π r 2 (Area is π x radius squared) (t) = (A (t) = A(r(t)) = A(3t) = ( t 2 = t 2 | A(t) (A º r)(t) A(r(t)) A(3t) π( 3t ) π 9t | A(t) = 9 π t 2 | We have skipped the “middle man” and are going straight from time to area without calculating the radius.

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

View Full Document
C OMPOSITE F UNCTION V ISUAL | f(x) = 2x 2 + 3 g(x) = 4x 3 + 1 | (f º g)(1) | (f º g)(1) = (f(g(1)) | g(1) = 4(1) 3 + 1 = 5 | f(5) = 2(5) 2 + 3 = 2·25 + 3 = 53 | (g º f)(1) (1) = (g(f(1)) | (g º f)(1) = (g(f(1)) | f(1) = 2(1) 2 + 3 = 5 (5) = 4(5) 3 1 = 4·125 + 1 = 501 | g(5) 4(5) + 1 4 125 + 1 501
C OMPOSITE F UNCTIONS | f(x) = 2x 2 + 3 g(x) = 4x 3 + 1 | (f º f)(-2) | (f º f)(-2) = (f(f(-2)) | f(-2) = 2(-2) 2 + 3 = 2·4 + 3 = 11 | f(11) = 2(11) 2 + 3 = 2·121 + 3 = 245 | (g º g)(-1) | (g º g)(-1) = (g(g(-1)) ( ) = 4( ) 1 = + 1 = | g(-1) = 4(-1) 3 + 1 = -4 + 1 = -3 | g(-3) = 4(-3) 3 + 1 = 4(-27) + 1 = -107 )(x) | (f º g)(x) | (f º g)(x) = (f(g(x)) | (f(g(x)) = f(4x 3 + 1) = 2(4x 3 + 1) 2 + 3 | = 2(4x 3 + 1)(4x 3 + 1) + 3 = 2(16x 6 + 8x 3 + 1) + 3 | = 32x 6 + 16x 3 + 2 + 3 = 32x 6 + 16x 3 + 5

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

View Full Document
C OMPOSITE F UNCTIONS | f(x) = 2x 2 + 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 17

6_1_6_2_Presentation_0 - SECTION 6.1 AND 6.2 COMPOSITE...

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

View Full Document
Ask a homework question - tutors are online