Question

Consider the following functions.

f(x)=x+53 and g(x)=1x

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) =

Answer 1

@vocaloid

Answer 2

remember, open circle means take the second function and plug it into the first function

so for (f∘g)(x), take g(x) = 1x and plug it into f(x) = x + 53

(the g(x) replaces the x inside f(x))

Answer 3

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

= (1/x) + 5 / 3

Answer 4

is that right

Answer 5

oh, is g(x) = 1/x? if so, yes

Answer 6

for the final answer as it asks (f∘g)(x) = ?

Answer 7

yes

if g(x) = 1/x, and f(x) = x + 53

then (f∘g)(x) = 1/x + 53 as you determined

Answer 8

it says two decimal places

Answer 9

oh, it's also asking for the domain

because you have x in the denominator of an expression, x cannot be 0, so it's every real value except 0

idk why they're asking to round to 2 decimal places though, I'm not sure what you're supposed to enter

Answer 10

it's not letting me put 1/x + 53 , it said incomplete

Answer 11

right

Answer 12

function seems right, I don't know what their issue is

domain is all real values except 0, in set notation it's (-∞,0) ∪ (0,∞)

Answer 13

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)=−x^√-x^3−5+4

g(x) =

h(x) =

Answer 14

possible to get an image of this? having trouble parsing this function

Answer 15

yes, a bit as it is difficult really

Answer 16

i can't get it , i get mixed up

Answer 17

can you take a screengrab of the function, or use latex to type it out exactly as it appears?

Answer 18

oh this isn't too bad, actually

let's let h(x) be the inner part of the root function (-x^3 - 5), that way we can make g(x) simply \[\sqrt[3]{(x)}+4\]

notice how when you plug in h(x) = -x^3 - 5 into that g(x), you get g(x) = (cube root of -x^3 - 5) + 4 which is your f(x)

Answer 19

-x^3 + 3sqrtx - 1

Answer 20

is this a new problem or are you still attempting the previous one

Answer 21

no , i thought you meant simplify 3sqrt(x) + 4 above and that was somewhat the answer

Answer 22

when it asks "Given f(x), find g(x) and h(x) such that f(x)=g(h(x)) "

it is asking for two separate functions, g(x) and h(x). once you figure out what your g(x) and h(x) are, that's it, enter what you got as your g(x) and h(x)

Answer 23

f(x)=3-x^3-5+4

Answer 24

remember, it is asking for g(x) and h(x)

it already tells you what f(x) is

Answer 25

h(x) = -x^3 - 5

Answer 26

good, and g(x)?

Answer 27

g(x) = 3sqrtx-5

Answer 28

almost

notice how f(x) = cube root(-x^3 - 5) + 4
if you choose h(x) = -x^3 - 5 (the expression inside the cube root)
then g(x) has to be cube root(x) + 4, not -5, in order to get f(x)

Answer 29

that's right

Answer 30

g(x) = 3sqrt+4

Answer 31

g(x) = \[\sqrt[3]{x}+4\]
make sure to put the cube root, not square root

Answer 32

yes sir , oh excuse me are you a male or female to say that too ?

Answer 33

if you don't mind me asking

Answer 34

I'm a woman

Answer 35

oh , i apologize . forgive me .

Answer 36

Yes ma'am

Answer 37

I tried to put it in the answers but it told me this otherwise