Question

Find (f∘g)(1) for the following functions.

f(−3)=4 and g(1)=−3

(f∘g)(1) =

Answer 1

@vocaloid

Answer 2

(f∘g)(x) = f(g(x))

plug x into g(x), plug the end result of g(x) as the x-value of f(x)

so in our case (f∘g)(1), we take g(1) = -3
the next step would be to take this output -3, and plug x = -3 into f(x), which they have already said is f(-3) = 4

so (f∘g)(1) = f(g(1)) = f(-3) = 4

Answer 3

i'm thinking the domain would be [4, ∞)

Answer 4

yup good

for the actual function, you can just add -4x + sqrt(x-4), I don't think you can really simplify beyond that

Answer 5

like, you would just write -4x + sqrt(x-4), you can't really combine these terms beyond that

Answer 6

i didn't find no solution

Answer 7

correct

Answer 8

same one but different

Answer 9

Consider the following functions.

f(x)=−4x and g(x)=√x−4

Find the formula for (f/g)(x) and simplify your answer. Then find the domain for (f/g)(x). Round your answer to two decimal places, if necessary.

(f/g)(x) =

Domain =

Answer 10

\[\sqrt{x-4} + -4x\]

i think this is right

Answer 11

(f/g)(x) means divide f(x) by g(x)
\[\frac{ -4x }{ \sqrt{x-4} }\]

for the domain, remember that
1. the denominator cannot be 0
2. square roots cannot be negative

Answer 12

oh yes ma'am

Answer 13

oh that wasn't right

Answer 14

did it tell you which part was wrong? what did you enter for the domain?

Answer 15

[4, ∞)

Answer 16

putting sqrt(x-4) in the denominator changes things

when sqrt(x-4) was in the numerator, x *could* be exactly 4, because sqrt(4-4) = 0 is valid

however, you cannot have x = 4 if sqrt(x-4) is in the denominator, because you cannot divide by 0

so the domain becomes (4, infinity)

open bracket around 4, not a closed bracket

Answer 17

alright you was right

Answer 18

Consider the following functions.

f={(2,4),(3,−2),(−5,−5)}
and

g={(−3,1),(−2,5),(3,−2)}

Find (f+g)(3)

(f+g)(3) =

Answer 19

look at the points in the lists

f(3) means the value of f at x = 3. this means the x-coordinate is 3. looking at the list of points, we have (3,-2) which means x = 3 and f(3) = -2. so f(3) = -2.

repeat this process with the g list.

then add the results.

Answer 20

1+4 = 5
-2 + 3 = 1
5 + -2 = 3
3 + -5 = -2
-2 + -5 = -7

Answer 21

you only need to find the value of g(3)

looking at the list of points in g: g={(−3,1),(−2,5),(3,−2)}

(3,-2) is the only point we need, because we only need g(3). (3,-2) means g(3) = -2

so we have f(3) = -2
and g(3) = -2

so (f+g)(3) = -2 - 2 = -4

Answer 22

i can't put the equal sign in there and i see

Answer 23

(f+g)(3) = -4, so you would just put -4

Answer 24

Consider the following functions.

f={(2,4),(3,−2),(−5,−5)}
and

g={(−3,1),(−2,5),(3,−2)}

(f−g)(3).

Answer 25

(-5, -5)

Answer 26

your answer should only be one number

we determined that f(3) = -2 and g(x) = -2

so (f-g)(3) is (-2) - (-2) = 0

Answer 27

Consider the following functions.

f={(2,4),(3,−2),(−5,−5)}
and

g={(−3,1),(−2,5),(3,−2)}

Find (fg)(3).

Answer 28

can you take a screengrab of this one too, I just want to check whether they want the product or the composite

Answer 29

is there an open circle between f and g (f⚬g?) or f*g? or just fg?

Answer 30

fg

Answer 31

oh in that case you just multiply f(3) * g(3) or just (-2)(-2) = 4

Answer 32

f(3) * g(3) = 9fg

that's what i got

Answer 33

but it's probably 4

Answer 34

f(3) is not the same as 3*f

f(3) means the value of f at x = 3

as we determined before, because (3,-2) is a point on f(x), that means f(3) = -2
likewise, because g has the point (3,-2), that means g(3) = -2

so (fg)(3) = -2 * -2

Answer 35

okay what would i apply because it wasn't right when i put -2 in

Answer 36

g(3) is -2
f(3) is -2

which means (fg)(3) = -2 * -2 = 4

Answer 37

Consider the following functions.

f={(2,4),(3,−2),(−5,−5)}
and

g={(−3,1),(−2,5),(3,−2)}

Find (f/g)(3).

Answer 38

(f/g)(3) is f(3) / g(3) = (-2) / (-2) = 1

Answer 39

Given f(x), find g(x) and h(x) such that f(x)=g(h(x)) and neither g(x) nor h(x) is solely x.

f(x)=1/4x+2

g(x) =

h(x) =

Answer 40

try making h(x) = 1/4x
if f(x) = g(h(x)) = 1/4x + 2, what does g(x) need to be?

Answer 41

1/2(2x + 1)

Answer 42

hmmm not quite

remember, g(h(x)) means take h(x), put it as the x-value into g(x)

so if h(x) = (1/4)x, let's try making g(x) = x + 2

if we plug in "(1/4)x" as x into g(x) = x + 2, we get g(h(x)) = (1/4)x + 2, which is the exact f function that we need

so one possible answer to this question is h(x) = (1/4)x and g(x) = x + 2

Answer 43

oh okay , i couldn't put (1/4) in

Answer 44

\[\frac{ 1 }{ 4 }x\]

Answer 45

it still show it's wrong

Answer 46

wait is the denominator 4x + 2?

Answer 47

for gx or hx ?

Answer 48

for the original function f(x)

can you take a screengrab of this one

Answer 49

oh yes , i'll send u one

Answer 50

ok, f(x) = 1 / (4x + 2) , with 4x + 2 in the denominator

let's try making h(x) = 4x + 2

in order for g(h(x)) = 1 / (4x + 2), what does g(x) need to be? how do we get the division in the problem?

Answer 51

g(x) needs to be where the number is known to be placed at to be sovled and the division is by hx and gx

Answer 52

if f(x) = 1 / (4x + 2)
and h(x) = 4x + 2

and f(x) = g(h(x)) = 1 / (4x + 2),

that means g(x) = 1/x

notice how we can plug in h(x) = 4x + 2 into g(x) to get 1 / (4x + 2)

Answer 53

oh i see g(x) = 1/x

Answer 54

is that true

Answer 55

yes. I picked h(x) = 4x + 2 and then I determined that g(x) must be 1/x in order for f(x) = g(h(x)) to be 1 / (4x + 2)

Answer 56

oh okay