Question

Am I correct? o:
I think it's either A or C but I feel it's A..

Answer 1

Actually it's D.

Answer 2

X could be anything, there is no limit on domain.

so all real number.

Answer 3

Oh.. because it's in the negatives and positives?

Answer 4

do you know what domain is?

Answer 5

Not 100%

Answer 6

The domain of a function is the set of all possible input values
(often the "x" variable)

Answer 7

x is "input variable"
makes sense? so for this function F(x), the possible of input value are unlimited. anything is possible so it's D

Answer 8

Got it!!

Answer 9

Thank you so much :)

Answer 10

Would I be correct in this one?

Answer 11

Close. it's (x-2)^2

it can be written as (x-h)^2 + k where h would drag function horizontally and k drag function vertically.

Answer 12

Oh yes yes I remember now!

Answer 13

so for x^2 - 2, function would be like this:

Answer 14

so is everything clear?

Answer 15

Yes on that one:) I got it! Thank you so much! Can you help me on this one?.. I have NO IDEA where to start or how to do it /:

Answer 16

G( F(x) ) basically means you replace in G(x) from x to F(x)

Answer 17

So A?

Answer 18

So we were given that G(x) = (x+3)^2

So G( F(x) ) = (F(x) + 3)^2

Answer 19

Yes it's A.

Answer 20

Oh I get it now, that's easy haha.

Answer 21

yeah. algebra is actually simple if you know what you are doing haha

Answer 22

you can't be good cooker if you don't know how to cook lol

Answer 23

So would this be (x-4)^2?

Answer 24

not quite

Answer 25

(x-4)^2 is x^2 shifted 4 units to right.

Answer 26

we need 4 unit down

Answer 27

So what is that formula?

Answer 28

remember? (x-h)^2 + k

Answer 29

basically f(x - h) + k, where h would shift f(x) horizontally and k would shift f(x) vertically.

Answer 30

oh oh! So it's (x+0)-4?

Answer 31

(x+0)^2-4
yep!

Answer 32

Oh yes! That's what I meant I have the formula right here haha. Thanks!:)

Answer 33

lol no problem, glad I helped.

Answer 34

Apparently it's just x^2-4... lol.

Answer 35

yeah. because x+0 is same as x lol

Answer 36

Now this one would be C right?

Answer 37

Because it's asking for range.

Answer 38

yeah, range is like domain, but instead of input, it's output.

so if it is C, that mean y can only be from 3 to -3.

look at graph. do you think it is true?

Answer 39

No that's incorrect so it would be B!

Answer 40

yep. B

Answer 41

I don't remember how to do these /: Could you walk me through?

Answer 42

basically, you can find inverse function by switch x and y to each other in original function, then isolate y.

for example. g(x) = y = 2x+6
to find inverse of g(x), you do like this:
x = 2y - 6

Answer 43

x+6 = 2y
x/2 + 3 = y

Answer 44

does that make sense?

Answer 45

Yes I believe so.. So the answer would end up being y=x/2+3?

Answer 46

no, it's not answer. it's just a explain.

let do actually one, shall we?

F(x) = y = 4x - 3

Answer 47

so first we switch x and y to each other

x = 4y - 3

Answer 48

then isolate y.

Answer 49

in explain, I mean g(x) = y = 2x - 6
sorry!

Answer 50

Okay so y=2x-6

Answer 51

Okay I believe I understand how to do that now..

Answer 52

no, no. it's example

it's not answer to this question

Answer 53

I know.. It's the answer to your example:)

Answer 54

ok lol sorry, just want to make sure.

so do you know what answer is for actual question?

Answer 55

x=4x-3
switch it around
y=4y-3
isolate
so y=.... I'm lost /:

Answer 56

F(x) is same as y

so we start with y = 4x - 3

Answer 57

switch it around:
x = 4y - 3

Answer 58

Oh got it! So switch around would be..
x=4y-3

Answer 59

yeah now isolate y

Answer 60

Isolate the y... So,
y=x-3/4?

Answer 61

I'm confused here...

Answer 62

ok, so we need to isolate y. we need to left term with y alone first,

so we need to move -3 to other side. how?

Answer 63

Add 3 to each side.

Answer 64

right. so

x + 3 = 4y - 3 + 3
x + 3 = 4y

Answer 65

but 4 is still with y. y need to be alone. what to do?

Answer 66

Then divide everything by 4

Answer 67

right!

Answer 68

so y=x/4+3/4? lol

Answer 69

yeah. that's your answer

Answer 70

Am I correct?

Answer 71

wait. question is little tricky.

it wants \(F^{-1}(y)\), not \(F^{-1}(x)\)

so answer should be y/4 + 3/4 lol...

Answer 72

yeah. you are right. y>= 2

Answer 73

Yeah I got that one wrong haha.. :)

Answer 74

yeah sorry.

Answer 75

What about this one?:P And no need to be sorry at all!

Answer 76

what's the possible input?

x can only be between -2 to 2?

Answer 77

Wait would it be all real numbers?...

Answer 78

sometime it's best to think what x cant be instead of what x can be.

Answer 79

do you think that? actually there is exactly one that cannot be possible.

Answer 80

Is that one C?

Answer 81

function is 1/( x - 2 ) right?

what x cant be, x = 2 because it would cause denominator to be zero. so x cannot be 2

yeah. C

Answer 82

Okay got it.. So it's A,B, or D.. But then A isn't it either so either B or D correct?

Answer 83

for this question? it is C. x can be anything, except 2. because otherwise there will be zero in denominator.

f(2) = \(\dfrac{1}{(2) - 2} = \dfrac{1}{0}\)

Answer 84

answer is C.

Answer 85

sorry. i messed up... f(x) is 1/(x + 2)

Answer 86

so x cannot be -2

Answer 87

I got it.. Haha:)