Question

Find (fgh)(-2) if f(x) = x2 - 5, g(x) = 3x + 1, h(x) = x + 3.

fgh(-2)=

Answer 1

firstly Substitute -2 in H(x) and then substitute the answer in g(x) and then that answer in f(x)

Answer 2

h(x) =1

Answer 3

yes put that in g(x)

Answer 4

f(x)= -1 right ?

Answer 5

Yes @alyygirl

Answer 6

ok then what

Answer 7

g(x) = -5

Answer 8

That is it -1 is ur answer

Answer 9

ok

Answer 10

im also confused about this

Answer 11

What is the confusion?

Answer 12

hold on

Answer 13

ok

Answer 14

do you understand that ?

Answer 15

I'm trying to .. Juz wait

Answer 16

ok thanks

Answer 17

Ooo interesting problem =o

Answer 18

yea Its weird huh

Answer 19

\[\Large\rm g(\color{red}{h(-1)})\]Your inner function is being evaluated at x=-1.
So trace the red line over to x=-1, what is the output value? the y-value?

Answer 20

h(-1 ) = -3 Ii guess

Answer 21

and g(-3) = 3

Answer 22

So answer will be 3 for first part

Answer 23

just 3 for (gh)(-1)=3?

Answer 24

We know y=f(x)
So we have are given with x which is -1 ..
From graph we find value of y for h(-1) and so on

Answer 25

Yes @alyygirl

Answer 26

ok and (f h g) (-4) =

Answer 27

-12 times f?

Answer 28

How -12 ?

Answer 29

-3 times 4?

Answer 30

whats f?

Answer 31

at h(-4) we have the value y=2
then g(2)=3
and f(3)=-4
so i guess -4 is the answer .. i hope i am not wrong

Answer 32

-4 for the second part? and 3 the first part

Answer 33

ill trust your answer better then mine lol

Answer 34

lOL Yea... -4 for 2nd part and 3 for first... Is this some sort of test or quiz

Answer 35

its online math class

Answer 36

no practice

Answer 37

it sucks

Answer 38

Ahhh okay Good luck then .. and lemme know if my answers were correct

Answer 39

ok I will :)

Answer 40

you there?

Answer 41

He is offline :c
sup?

Answer 42

i dont understand this

Answer 43

Understand what? The graph problem with the composition stuff?

Answer 44

lolol did you take a picture of your computer screen? :3
it's all tilted. dat's funny.

Answer 45

yea cuz you cant type it haha

Answer 46

I wish this was easy omg

Answer 47

So yah, piece-wise functions can be a little weird.
It's one of the three pieces, depending on where our x is at that given moment.

So when our x is -2, which piece do we want to use?
(Look at the intervals on the right)

Answer 48

the second one

Answer 49

So the first and second piece both mention -2.
But it looks like the first piece has the `or equal to`, doesn't it?

Answer 50

yes

Answer 51

Ok so when x=-2, our function becomes:\[\Large\rm f(\color{orangered}{x})=(\color{orangered}{x})^2+4\]

Answer 52

\[\Large\rm f(\color{orangered}{-2})=(\color{orangered}{-2})^2+4\]

Answer 53

f(-2)=8

Answer 54

yay!

Answer 55

thats it? or no

Answer 56

Yes that solves your first blank.

Answer 57

nice not bad

Answer 58

Any confusion on how our function simply became: \(\Large\rm f(\color{orangered}{x})=(\color{orangered}{x})^2+4\)
?

Answer 59

When x is AT or below -2, we use that specific piece to evaluate.

Answer 60

What do you think for the next one? :U

Answer 61

let me see

Answer 62

f (3) 2x+3?

Answer 63

Check your intervals carefully.
You seem to keep wanting to go to that middle one for some reason.

Answer 64

ok

Answer 65

If x=3, that means x is larger than 1, right?
It's not between -2 and 1.

Answer 66

ok

Answer 67

shoot ok so f(3)= 2x(3)+3

Answer 68

Im guessing this is wrong?

Answer 69

Yes :(
You went to the middle piece again........

Answer 70

The BOTTOM PIECE corresponds to x values larger than 1, yes?

Answer 71

ok yea

Answer 72

so its square root x+1 equation we use

Answer 73

Yes.

Answer 74

f(3) = square root3x +1

Answer 75

I guess you're having a little trouble with function notation.
Try to understand the colors I'm using here,

So when \(\Large\rm x\gt1\),\[\Large\rm f(\color{orangered}{x})=\sqrt{\color{orangered}{x}+1}\]\[\Large\rm f(\color{orangered}{3})=\sqrt{\color{orangered}{3}+1}\]See how we're REPLACING each orange with 3?
The x's get `replaced` with 3.

You shouldn't have a 3x anywhere.

Answer 76

ok 12?

Answer 77

3+1 =4*3=12

Answer 78

where is the 4*3 step coming from?

Answer 79

adding inside the the square root and multiplying 3?

Answer 80

Did you read my comment that I made?
You should not having a 3x anywhere.
You should only have a 3.

`THE 3 IS REPLACING YOUR X`

Answer 81

ok got it

Answer 82

it 2

Answer 83

yay good job!

Answer 84

ok good :)

Answer 85

so thats the second box

Answer 86

now for the last one we use the middle?

Answer 87

equation

Answer 88

Yes we FINALLY get to use the middle one ;) lol

Answer 89

The interval for the middle piece INCLUDES -1, see the `or equal to` sign on the 1?

Answer 90

lol

Answer 91

So yes middle.

Answer 92

yes

Answer 93

Not -1, I mean 1, sorry.

Answer 94

yea

Answer 95

is the answer for the last 0