1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words...

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1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing for all x, then f has an inverse. 3)Why does y = x 2 not really have an inverse?

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Transcript of 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words...

Page 1: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.

1) Given f(x) = x5 + 8x3 + x + 1 has an inverse, find f-1(1) and f-1(11).

2) Explain, in words and a picture, why this is true: if f(x) is increasing for all x, then f has an inverse.

3) Why does y = x2 not really have an inverse?

Page 2: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.

Unit Circle1) Draw a large circle, centered at the origin.2) Label the coordinates of the circle at the axes.3) Draw in radii at every 45° measure then label all

the radians for these degrees.4) Draw in radii at every 30° measure then label all

the radians for these degrees.5) Draw on your paper an equilateral and isosceles

right triangles.6) See if you can remember the rules on these

special triangles.

Page 3: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.
Page 4: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.
Page 5: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.
Page 6: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.
Page 7: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.
Page 8: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.
Page 9: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.
Page 10: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.
Page 11: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.
Page 12: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing.

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Derivatives Part A. Review of Basic Rules f(x)=xf`(x)=1 f(x)=kx f`(x)= k f(x)=kx n f`(x)= (k*n)x (n-1) 1.) The derivative of a variable is 1. 2.)

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Introduzione al problema Sia assegnata una funzione f(x) di cui sono noti i valori f(x 1 ), f(x 2 ),…,f(x N ) nei punti x 1, x 2, …, x N per semplicità

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LESSON 8.1 N Practice A AME ATEmathwithhinz.weebly.com/uploads/5/4/2/1/54211207/unit_e_packet.p… · f"x#! 1 3 e3"x $ 1 2 e2x$1" 5 f"x#! 1 f"x#! 2ex"4 $ 1 f"x#! 2e3x $ 1 4 e"x" 2

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Activité Mentale - Sésamath...Question no 4 Calculer : f(x)+5 avec x =3 et f(x)=x2 +1 f(x +5) avec x =3 et f(x)=x2 +1 Activité Mentale 30

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 · 1 แบบฝึกหัด 1.1 1) 1.1 Fx x 322 f x ดังนั้น F เป็นปฏิยานุพันธ์ของ f และปฎ f

 · 1 แบบฝึกหัด 1.1 1) 1.1 Fx x 322 f x ดังนั้น F เป็นปฏิยานุพันธ์ของ f และปฎ f

-2 -1 2 0 1 · 2019-10-31 · 0202 1 f x² 5x 21 f(x) x² 1 D 1;1 f ^` 3x² 4x 52 f(x) (x 2)² D2 f ^ 4x 8 3 f(x) x² 4x 3 f(x) x² 4x 5 D 1;3 f ^ ` 4 D f x² 15 f(x) x1 D 1; f f@

-2 -1 2 0 1 · 2019-10-31 · 0202 1 f x² 5x 21 f(x) x² 1 D 1;1 f ^` 3x² 4x 52 f(x) (x 2)² D2 f ^ 4x 8 3 f(x) x² 4x 3 f(x) x² 4x 5 D 1;3 f ^ ` 4 D f x² 15 f(x) x1 D 1; f f@

1.- f x x gx hx x

1.- f x x gx hx x

-3 -4 1 -4 · 2021. 1. 2. · 0,1 D D @ 1;1> f(x) 0 @2;3> f(x) 0 f a 1 a1 f(x) x² 3x 2 a1f(x) 4 x ...

-3 -4 1 -4 · 2021. 1. 2. · 0,1 D D @ 1;1> f(x) 0 @2;3> f(x) 0 f a 1 a1 f(x) x² 3x 2 a1f(x) 4 x ...

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This time (f+g)(x)=f(x)+g(x) (f-g)(x)=f(x)-g(x) (fg)(x)=f(x)*g(x) (f/g)(x)=f(x)/g(x), g(x)≠0 (f ∘ g)(x)=f(g(x))

This time (f+g)(x)=f(x)+g(x) (f-g)(x)=f(x)-g(x) (fg)(x)=f(x)*g(x) (f/g)(x)=f(x)/g(x), g(x)≠0 (f ∘ g)(x)=f(g(x))

INTEGRALS - samagra.itschool.gov.in · ∫ f x dx( ) Integral of f with respect to x f(x) in ... –1 2 sin C 1 dx x – x ...

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(A) f x) = 0 (B) f x) = x3 +2 (C) f x) = 1 (D) y x) = x 5 ...

(A) f x) = 0 (B) f x) = x3 +2 (C) f x) = 1 (D) y x) = x 5 ...

Name: Class: Date: 1 x and f x and f x

Name: Class: Date: 1 x and f x and f x

1 titul 1-2 - ММФ КНУ...f(x,y), u(x,y) Функції двох змінних x, y b a f f(b) − f(a) β α ∫f x d x( ) Інтеграл від f(x) на відрізку

1 titul 1-2 - ММФ КНУ...f(x,y), u(x,y) Функції двох змінних x, y b a f f(b) − f(a) β α ∫f x d x( ) Інтеграл від f(x) на відрізку

Karl Byleen · Karl Byleen 1.f(x) = 1 = x-1 x f’(x) =-x-2 (Using Power Rule) f”(x) = 2x-3 6 f (3) (x) = -6x-4 = -x 4 2. f(x) = ln(1 + x) 1 = (1 + x)-1 f'(x) = 1 x f"(x) = (-1)(1

Karl Byleen · Karl Byleen 1.f(x) = 1 = x-1 x f’(x) =-x-2 (Using Power Rule) f”(x) = 2x-3 6 f (3) (x) = -6x-4 = -x 4 2. f(x) = ln(1 + x) 1 = (1 + x)-1 f'(x) = 1 x f"(x) = (-1)(1