Warm Up Let f(x) 5x + 1 and g(x) √x. a.Is f(g(x)) continuous at x 3? b.Is f(g(x)) continuous at...

download Warm Up Let f(x) 5x + 1 and g(x) √x. a.Is f(g(x)) continuous at x 3? b.Is f(g(x)) continuous at x 0? c.Is g(f(x)) continuous at x 3? d.Is g(f(x))

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7.3 – Power Functions & Function Operations. Operations on Functions: for any two functions f(x) & g(x) 1. Addition h(x) = f(x) + g(x) 2. Subtraction.

7.3 – Power Functions & Function Operations. Operations on Functions: for any two functions f(x) & g(x) 1. Addition h(x) = f(x) + g(x) 2. Subtraction.

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

Introduction F G x R¡ G

Introduction F G x R¡ G

1-6 Function Operations and Composition of · PDF fileFind ( f + g)(x), (f ± g)(x), (f { g)(x), and (x) for each f(x) and g(x). State the domain of each new function. f(x) = x2 +

1-6 Function Operations and Composition of · PDF fileFind ( f + g)(x), (f ± g)(x), (f { g)(x), and (x) for each f(x) and g(x). State the domain of each new function. f(x) = x2 +

1.8 Combinations of Functions: Composite Functions. 84-92.pdf · f g x f x g x 2x 1 x2 2x 1 x2 4x f x 2x 1 g x x2 2x 1, f g x. ... Sum, Difference, Product, and Quotient of Functions

1.8 Combinations of Functions: Composite Functions. 84-92.pdf · f g x f x g x 2x 1 x2 2x 1 x2 4x f x 2x 1 g x x2 2x 1, f g x. ... Sum, Difference, Product, and Quotient of Functions

M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)

Algebra 2: Checkpoint 6.3 & 6.4 1.Let f(x)=5x-3 and g(x)= -x 2 +2. Find the following. a. g(f(-2))b. f(g(x)) 2. Find the inverse of each function. a.

Algebra 2: Checkpoint 6.3 & 6.4 1.Let f(x)=5x-3 and g(x)= -x 2 +2. Find the following. a. g(f(-2))b. f(g(x)) 2. Find the inverse of each function. a.

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)

Theorem 1 The chain rule If k(x) =f (g(x)), then k’(x) = f ’ ( g(x) ) g’(x)

Theorem 1 The chain rule If k(x) =f (g(x)), then k’(x) = f ’ ( g(x) ) g’(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 ●

g x f x s g x y e s ce f x 0 s em y d f x g x f x 0 d e g x n em g f p at … · 2016-07-06 · g g s n. 6 u s f a . 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5

g x f x s g x y e s ce f x 0 s em y d f x g x f x 0 d e g x n em g f p at … · 2016-07-06 · g g s n. 6 u s f a . 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5

BY DR. JULIA ARNOLD The Algebra of Functions What does it mean to add two functions? If f(x) = 2x + 3 and g(x) = -4x - 2 What would (f+g)(x) be? (f+g)(x)

BY DR. JULIA ARNOLD The Algebra of Functions What does it mean to add two functions? If f(x) = 2x + 3 and g(x) = -4x - 2 What would (f+g)(x) be? (f+g)(x)

 · 2015-03-24 · f(x) = x xeDf -1-2 xeDf f(x)- y=1-2 Y=y-l f(x) x E Dg -xeDg XEDg I-XI-2 -2 Ixl-2 g(x) = -2 g(x) g(x) = f(x) g(x) 5 vvv.KorrQsQty.B1093pot.Com . 8-1 X-I 1- x- g(x

 · 2015-03-24 · f(x) = x xeDf -1-2 xeDf f(x)- y=1-2 Y=y-l f(x) x E Dg -xeDg XEDg I-XI-2 -2 Ixl-2 g(x) = -2 g(x) g(x) = f(x) g(x) 5 vvv.KorrQsQty.B1093pot.Com . 8-1 X-I 1- x- g(x

6.1 The Composition of Functions f o g - composition of the function f with g is is defined by the equation (f o g)(x) = f (g(x)). The domain is the set.

6.1 The Composition of Functions f o g - composition of the function f with g is is defined by the equation (f o g)(x) = f (g(x)). The domain is the set.

Given f(x)= 3x-x and g(x)=5x+2 Evaluate a) f(2) b)g(3-x) c)f(4)+g(8) d)f(3) * g(1) e)g(y+2)

Given f(x)= 3x-x and g(x)=5x+2 Evaluate a) f(2) b)g(3-x) c)f(4)+g(8) d)f(3) * g(1) e)g(y+2)

 · 1 x (l x g g l l l x ( l f l g g l g g l (H l l ! g l g g ( m " l x g # ( m l x %$ g & l 2 ') * "!, + + m ! g

 · 1 x (l x g g l l l x ( l f l g g l g g l (H l l ! g l g g ( m " l x g # ( m l x %$ g & l 2 ') * "!, + + m ! g

Definition: Let f and g be two functions such that x g x f g f1.9 Inverse Functions Definition: Let f and g be two functions such that f g x x for every x in the domain of g and g

Definition: Let f and g be two functions such that x g x f g f1.9 Inverse Functions Definition: Let f and g be two functions such that f g x x for every x in the domain of g and g

Do Now If f(x) = 2x + 3 and g(x) = x 2 – 2x, find: 1)f(3)2)g(-2) *3) g(4) – f(1)

Do Now If f(x) = 2x + 3 and g(x) = x 2 – 2x, find: 1)f(3)2)g(-2) *3) g(4) – f(1)

Operations on Functions Lesson 2.5 ƒ(g(x)) f(x) + g(x) f(x) - g(x) f(x) ÷ g(x) f(x) ∙ g(x)

Operations on Functions Lesson 2.5 ƒ(g(x)) f(x) + g(x) f(x) - g(x) f(x) ÷ g(x) f(x) ∙ g(x)

Splash Screen. Concept Example 1 Add and Subtract Functions A. Given f(x) = 3x 2 + 7x and g(x) = 2x 2 – x – 1, find (f + g)(x). (f + g)(x)=f(x) + g(x)Addition.

Splash Screen. Concept Example 1 Add and Subtract Functions A. Given f(x) = 3x 2 + 7x and g(x) = 2x 2 – x – 1, find (f + g)(x). (f + g)(x)=f(x) + g(x)Addition.