Question

Find (f∘g)(−4) for the following functions.

f(x)=3x−3 and g(x)=x^2

(f∘g)(−4) =

Answer 1

@vocaloid

Answer 2

(f∘g)(x) with an open circle means

f(g(x)). Take the value of g(x) and plug it into f(x).

So with this problem, you’ll calculate g(x) for x = -4

You’ll then take that result, plug it into f(x) as the x-value

Answer 3

f(x-4)
3(x+x^2) + -3

is this right

Answer 4

?

Answer 5

start with g(x) first

calculate g(x) at x = -4

g(x) = x^2 = (-4)^2 = 16

then take x = 16 and plug it into f(x)

Answer 6

f(16) = x^2 = (-4)^2 =

Answer 7

g(-4)=16

(f∘g)(−4) =

Answer 8

g(-4) = 16

now take x = 16 into f(x)

f(x)=3x−3 = 3(16) - 3 = 45 ---> your solution

Answer 9

thank you

Answer 10

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.

Answer 11

\[f(x) = \frac{ 2 }{ 5x-1}\]

g(x) =

h(x) =

Answer 12

these types of problems are a bit hard to teach, because there's not really just one possible answer to them

for this one, I notice that we have 2 / (5x - 1)

I'll let g(x) = 2 / x, that way, I can let h(x) = 5x - 1

so that, when h(x) is put into g(x), we get f(x) = g(h(x)) = 2 / (5x - 1)

you kind of have to work backwards and see how you can split the whole function into pieces

Answer 13

I understand

Answer 14

\[f(x) = 2\sqrt{5x-1}\]

Answer 15

i know we have to substitute h(x)=x in the above function.

Answer 16

is this the same type of problem? decompose f(x) into g(x) and h(x)?

let's break down f(x) into it's two parts: 2 multiplied with sqrt(5x-1)

so we can just let g(x) = 2x and h(x) = sqrt(5x-1), notice how f(x) = g(h(x)) becomes 2sqrt(5x-1)

Answer 17

yes unless i entered it wrong

Answer 18

5/(5x - 1)^1/2

Answer 19

thoughts on this one? notice how it's just like the first problem f(x) = 2 / (5x - 1) and can be approached in a similar way

Answer 20

was what i entered was right above and put it in as the similar way like the first problem ?

Answer 21

wait - are we on the same problem? f(x) = 2sqrt(5x-1)?

Answer 22

yes , i'm sorry i'm making this confusion

Answer 23

is it still asking for f(x)=g(h(x))?

Answer 24

i believe so

Answer 25

because you have two things multiplied to each other, an easy way to do it is to let g(x) = 2x, and h(x) = sqrt(5x-1). that way, when you plug in h(x) into g(x), you get g(h(x)) = 2sqrt(5-1). because it asks for g(x) and h(x), just say what g(x) and h(x) are in your answer.

Answer 26

okay , do i need to set up g(x) first

Answer 27

2(x) = 2sqrt(5-1)

Answer 28

no, that's not quite how it works

it is asking to take the original function f(x) and come up with two functions g(x) and h(x) such that

f(x) = g(h(x))

once you figure out what g(x) and h(x) are, that's it, you just say what g(x) = and h(x) =

Answer 29

we came up with: g(x) = 2x, and h(x) = sqrt(5x-1), because when you take f(x) = g(h(x)) you get f(x) = g(h(x)) = 2sqrt(5x-1), which is the original function, so you just say that g(x) = 2x and h(x) = sqrt(5x-1)

Answer 30

ohhhh i see it now how you put it

Answer 31

You mean as Finding g(x) and h(x) such that f(x)=g(h(x)) and checking to ensure the composition of the terms chosen in previous steps equals f(x).

Is that right ?

Answer 32

g(x) = 2x and h(x) = sqrt(5x-1) is the answer ?