Question

composite functions

Answer 1

since it asks for f dot g, replace "x" with x^4 into f(x)

Answer 2

(x^4)^2 + 8(x^4) = ?

Answer 3

*** note: you are not given an x value so your answer should be a function not a number

Answer 4

is it x^8+8x^4?

Answer 5

yes, that's your answer ~

Answer 6

similar, take f(x) = 7x - 9 and replace "x" with "x^2"

Answer 7

7x^2-9

Answer 8

good, that's your ans

Answer 9

since h(x) = x^3 and f(x) = (4x^2 + 11)^3 then it's clear that g(x) is just the part inside the parentheses

Answer 10

im confused

Answer 11

so if f(x) = h dot g = (4x+11)^3
and h(x) = x^3
then g(x) is what gets replaced as x in h(x)

Answer 12

*** so g(x) = 4x^2 + 11 *** i made a typo in the pic

Answer 13

if we plug in x = 6 into g(x) what do we get?

Answer 14

3.5?

Answer 15

yeah, so since g(6) is a real number then it's in the domain of f dot g (answer choice 2)

Answer 16

if we plug x = 3 into g(x) what do we get?

Answer 17

-16

Answer 18

check your math again

-4(3) + 4 = ?

Answer 19

-8

Answer 20

good, now if x = -8 what does f(x) = ?

Answer 21

it says error bc u cant 2root a neg.

Answer 22

good, so 3 can't be in the domain of f dot g

Answer 23

ans choice 2

Answer 24

x = 5, g(x) = ?

Answer 25

-49?

Answer 26

good, and if x = -49, f(x) = ?

Answer 27

it cant

Answer 28

good, so 5 isn't in the domain of f dot g

Answer 29

same thing as before: x = -7, g(x) = ?

Answer 30

-68?

Answer 31

good, so if x = -68 then f(x) = ?

Answer 32

cant

Answer 33

good so -7 is not in the domain

Answer 34

g(x) has to be positive so x - 4 has to be positive

so x must be greater than 4

which choice matches?

Answer 35

5

Answer 36

good, that's your answer

Answer 37

g(x) has to be positive so x + 6 has to be positive, therefore x > -6

Answer 38

so which choice matches?

Answer 39

6

Answer 40

good, that's your answer

Answer 41

the minumum value of a square root function occurs when the inside of the radical is a 0

so x + 6 = 0
x = ?

Answer 42

-6

Answer 43

good so -6 = your ans

Answer 44

same thing as before, x - 6 = 0 so x = ?

Answer 45

6

Answer 46

good, so 6 = your ans

Answer 47

ok, since f(x) = 1/x, then x cannot be equal to 0

Answer 48

therefore: x^2 - 4x = 0

if you solve this you will get your answers

know how to do it?

Answer 49

no

Answer 50

start by factoring out x

x^2 - 4x

becomes

x(x-4) = 0

therefore:

x = 0 and x - 4 = 0 so x = ?

Answer 51

4

Answer 52

good, so 0 and 4 are your answers (include both)

Answer 53

same thing

x^2 - 6x = 0

x(x-6) = 0

x = 0 and x - 6 = 0 so x = ?

Answer 54

6

Answer 55

good, so 0,6 are your answers

Answer 56

subtract 4 from the x-coordinate

Answer 57

I'm a little uncertain but I would multiply the x-coordinate by 2

Answer 58

THAT WAS RIGHT

Answer 59

yeah I just realized you posted a similar question before and I accidentally gave you the wrong method :S

Answer 60

lol its cool i wouldve done it all wrong

Answer 61

if you have a fraction inside the parentheses you would multiply the x coordinate by the denominator

Answer 62

so I believe we would take the reciprocal and multiply the x-coordinate by (-4/3)

Answer 63

(-36,2)?

Answer 64

horizontal transformations were never my strong suit

Answer 65

hm

Answer 66

9*(-4/3) = ?

Answer 67

oh I thought u would have to multiply 9 by -4

Answer 68

yeah I should have mentioned that rule only applies when the numerator is 1

Answer 69

oh

Answer 70

otherwise I believe you're supposed to flip the fraction then multiply

Answer 71

9*(-4/3) = -12 so I ~think~ the answer is (-12,2)?

Answer 72

yup

Answer 73

divide the x-coordinate by 3

Answer 74

so (-8,-4)?

Answer 75

multiply the y-coordinate by (1/2)

Answer 76

the (1/2) is outside the parentheses so it's different

Answer 77

oh

Answer 78

if it's inside we change the x-coordinate, if it's outside we change y

Answer 79

(-4,-2)?

Answer 80

is this right bc i wasnt to sure on my calculating?

Answer 81

yeah that's the answer, good

Answer 82

same thing, multiply y by (1/2)

Answer 83

the y?

Answer 84

the y-coordinate, yeah

Answer 85

1,-4?

Answer 86

yup, that's the answer

Answer 87

i have on more lesson and its only 5 questions

Answer 88

sure go for it

Answer 89

we did something like this yesterday

airplane + wind = 1680/4
airplane - wind = 1680/5

solve for airplane by adding the equations together

Answer 90

1680+5=420
1680-5=336

Answer 91

?

Answer 92

hmm not quite

Answer 93

airplane + airplane = 2*airplane (or 2x if you want to use their variables)

Answer 94

1680/4 + 1680/5 = 756

Answer 95

wind - wind = 0

Answer 96

so 2*airplane = 756
airplane = ?

Answer 97

so the speed of the plane when theres no wind is 756?

Answer 98

nope not quite

Answer 99

2* airplane speed = 756
airplane speed = ?

Answer 100

378

Answer 101

is the answer?

Answer 102

yes, good

Answer 103

it's 25, we've done this one before :S

Answer 104

i think weve done most of these but i dont remeber the answers

Answer 105

load should be <= 150
mail should be <= 150000

Answer 106

"as many as" usually means <=

Answer 107

so the 2nd one?

Answer 108

yeah

Answer 109

burgers and bratwurst >= 90
budget <= 120

Answer 110

last one

Answer 111

more expensive tree >= less expensive tree
budget <= 95,000

Answer 112

which one would that be?

Answer 113

the more expensive tree is y
the less expensive tree is x

Answer 114

y >= x

budget <= 95,000

Answer 115

you can flip y>= x to get x<=y...