saylor.orgsaylor.org/.../uploads/2011/11/1-4CombinationsOfFunctions.pdf · Fig. 6 cc (a) f( g(x) )...

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Transcript of saylor.orgsaylor.org/.../uploads/2011/11/1-4CombinationsOfFunctions.pdf · Fig. 6 cc (a) f( g(x) )...

Page 1: saylor.orgsaylor.org/.../uploads/2011/11/1-4CombinationsOfFunctions.pdf · Fig. 6 cc (a) f( g(x) ) — f og(x) Fig. (b) g( f(x) ) = g o f(x) 5 I nput function f YVhich line of the
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ON SPACES OF FkNITE PARTS OF HOIOGEATEOUS FUNCTIO!S · kernel of the operator F is given by F(x, x--g): F(g)--- ! F(x, x-})rp(g)clg where F(x, ij) is a distribution expressed as F(x,

ON SPACES OF FkNITE PARTS OF HOIOGEATEOUS FUNCTIO!S · kernel of the operator F is given by F(x, x--g): F(g)--- ! F(x, x-})rp(g)clg where F(x, ij) is a distribution expressed as F(x,

Intuitions About Lagrangian Optimization · follows. Define the Lagrangian function F(x,λ) = f(x) + λ g(x), where λ is a real variable. If, among the points where g(x) = 0, f (x)

Intuitions About Lagrangian Optimization · follows. Define the Lagrangian function F(x,λ) = f(x) + λ g(x), where λ is a real variable. If, among the points where g(x) = 0, f (x)

f g Q m g N 5 q g i g d X G Û g & º ? û228 L ' º Ý g 4 3 ÷ p q } q \ f g T f Ú T } q \ f g Q m g N 5 q g i g d X G Û g n p M g - « p } q \ f « Q m « N 5 q « « d X G ¿

f g Q m g N 5 q g i g d X G Û g & º ? û228 L ' º Ý g 4 3 ÷ p q } q \ f g T f Ú T } q \ f g Q m g N 5 q g i g d X G Û g n p M g - « p } q \ f « Q m « N 5 q « « d X G ¿

x) · cot x = ¯csc 2 x d dx sec x = sec x tan x f(t) = 1 2 gt 2 + v 0 t + s0 v(t) = f'(t) a(t) = v'(t) = f"(t) d dx csc x = ¯csc x cot x d dx (f(x)⋅g(x))= f(x)g'(x)+ g(x)f'(x)

x) · cot x = ¯csc 2 x d dx sec x = sec x tan x f(t) = 1 2 gt 2 + v 0 t + s0 v(t) = f'(t) a(t) = v'(t) = f"(t) d dx csc x = ¯csc x cot x d dx (f(x)⋅g(x))= f(x)g'(x)+ g(x)f'(x)

Optimization. f(x) = 0 g i (x) = 0 h i (x)

Optimization. f(x) = 0 g i (x) = 0 h i (x)

Essential Question: How do you find the value of f(g(5)) and g(f(3)) given: f(x) = 3x + 1 and g(x) = 2x - 5.

Essential Question: How do you find the value of f(g(5)) and g(f(3)) given: f(x) = 3x + 1 and g(x) = 2x - 5.

Entry task Let g(x) be the indicated transformation of f(x). Write the rule for g(x). 4. f(x) = –2x + 5; vertical translation 6 units down g(x) = – 2x.

Entry task Let g(x) be the indicated transformation of f(x). Write the rule for g(x). 4. f(x) = –2x + 5; vertical translation 6 units down g(x) = – 2x.

Find ( f + g )(x f g )(x andFind ( f + g )(x), (f ± g)(x), (x),and x) for each f(x) and g(x). Indicate any restrictions in domain or range. 62/87,21 $16:(5 62/87,21

Find ( f + g )(x f g )(x andFind ( f + g )(x), (f ± g)(x), (x),and x) for each f(x) and g(x). Indicate any restrictions in domain or range. 62/87,21 $16:(5 62/87,21

Information Quality (InfoQ) - AfekaInfoQ(f,X,g) = U( f(X|g) ) Information Quality (InfoQ) 19 g A specific analysis goal X The available dataset f An empirical analysis method U A utility

Information Quality (InfoQ) - AfekaInfoQ(f,X,g) = U( f(X|g) ) Information Quality (InfoQ) 19 g A specific analysis goal X The available dataset f An empirical analysis method U A utility

3.7 Implicit Differentiation xf(x)f(x)g(x)g(x) f ‘ (x)g ‘ (x) 2821/3 33 33 4422 5.

3.7 Implicit Differentiation xf(x)f(x)g(x)g(x) f ‘ (x)g ‘ (x) 2821/3 33 33 4422 5.

1. f( g(x)) = ____ for g(x) = 2x + 1 and f(x) = 4x, if x = 3 2. (f + g)(x) = ____ for g(x) = 3x 2 + 2x and f(x) = 3x + 1 3. (f/g)(x) = ______ for f(x)

1. f( g(x)) = ____ for g(x) = 2x + 1 and f(x) = 4x, if x = 3 2. (f + g)(x) = ____ for g(x) = 3x 2 + 2x and f(x) = 3x + 1 3. (f/g)(x) = ______ for f(x)

Name:__________ warm-up 6-2 Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f – g)(x), if it exists. Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f ●

Name:__________ warm-up 6-2 Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f – g)(x), if it exists. Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f ●

Problem 1 2 g f g f g x h x f g x h - Home | University of ... · Problem 1 Consider the functions f(x)=x2 1 and g(x)= p x1. (a) Find the domains of functions f and g. Give your answers

Problem 1 2 g f g f g x h x f g x h - Home | University of ... · Problem 1 Consider the functions f(x)=x2 1 and g(x)= p x1. (a) Find the domains of functions f and g. Give your answers

lawhonmath.weebly.com · Web view1. f x =4x-1, g x = 6+7x 2. f x =5x+2, g x = x 2 -14x . 3. f x = x 2 -2x+1, g x =8-3 x 2 4. f x = x 2 +3, g x = 5+ x 2 . Compute f -1 (x) of the following

lawhonmath.weebly.com · Web view1. f x =4x-1, g x = 6+7x 2. f x =5x+2, g x = x 2 -14x . 3. f x = x 2 -2x+1, g x =8-3 x 2 4. f x = x 2 +3, g x = 5+ x 2 . Compute f -1 (x) of the following

f x - Gwinnett County Public Schools · f x x x 2 32 b. g x x 2 4 ; x 0 6. Verify which of the following are inverses of one another by considering f g x and g f x a. 4 4 f x x x

f x - Gwinnett County Public Schools · f x x x 2 32 b. g x x 2 4 ; x 0 6. Verify which of the following are inverses of one another by considering f g x and g f x a. 4 4 f x x x

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Copyright - Comic book · W&g??W&@g? W&@@g??W.Y@@g? W.Y?@@g??W.Ye@@g? W.Y?e@@g??W.Yf@@g??7Y?f@@g??@@@@@f? @@g? @@g?????W2@6Xg? W.M?I/X?f? 7He?N1?f? @?f@?f? @Le?J5?f? 3)K?O.Y?f?

Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now.

Describe or draw the graph of g(x), h(x) and p(x) if f(x) is the parent function: a) g(x)=f(x)+2 b) p(x)=f(x+2) c) h(x)=-f(x) Do Now.

201904240700 g thet oik math a - Syneirmos · g x f x x′ ′( ) ( )= − +2 1 . Επειδή g x g( ) ( )≤ 1 για κάθε x > 0 προκύπτει ότι η συνάρτηση

201904240700 g thet oik math a - Syneirmos · g x f x x′ ′( ) ( )= − +2 1 . Επειδή g x g( ) ( )≤ 1 για κάθε x > 0 προκύπτει ότι η συνάρτηση

f,g f f. f - askisopolis.gr · f x 3 4 2 5 xx ... 3f 101 2f 1001 f 10001 log18 6 28. f x ln e 1 x g x ln 2e 2 1x . f,g. f,g f 2x g x 1 ! . g 1 x f x ln2 29. f x log x 1 log x 2x 2

f,g f f. f - askisopolis.gr · f x 3 4 2 5 xx ... 3f 101 2f 1001 f 10001 log18 6 28. f x ln e 1 x g x ln 2e 2 1x . f,g. f,g f 2x g x 1 ! . g 1 x f x ln2 29. f x log x 1 log x 2x 2

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