Question

How would I start off finding the Domain and the Range of this question? (Question attached in next comment)

Answer 1

I'm thinking the domain is [2,3,4,5,6,7,8,9]

Answer 2

the domain are the numbers you can "put in" or give to the function and get back an answer.

Answer 3

\[ g \circ f \] means first feed a number to f, get an answer, and feed that answer to g to get the final answer.

notice that if we give f a number x and f returns a number that "g" does not understand (where g has no answer) then we have to exclude x from the domain

Answer 4

@phi I'm still kind of confused.

Answer 5

if you pick 3 for the input to f, f returns 1
do you agree ?

Answer 6

now if we ask what does g do when you give it a 1 ?
look in g's domain, and we see there is no 1. so g will not have an answer.
so we better not choose 3 if we expect \( g \circ f \) to have an answer.
in other words, we can only use the numbers in f's domain that will allow g to have an answer.

Answer 7

The domain of g is {2,3,4,6}, this mean the function g will only compute if one of these values is its input,

g∘f = g( f )

Only inputs to f that give these as outputs; to input into g, will work . ie they will be in the domain of g∘f

The domain is
Which values can be put into f, that will pass through g

Answer 8

it might help to draw some lines connecting the numbers in the range of f, with the same number (if it appears) in the domain of g,

of these lines , go backwards along the arrows to the numbers in the domain of f (that the arrow started at), these will be the domain of g∘f

Answer 9

@phi Yes, I agree.

Answer 10

@phi @unklerhaukus OpenStudy would not load for me for the longest and it still is having problems. But I've read both of your responses and now understand better. For the range, based off of what was said, I'm assuming it comes out to {0} because none match up.

Answer 11

I need verification on the answer to the range please.

Answer 12

2, 4, and 6 are common to the range of f and domain of g

Answer 13

the domain of g∘f are the inputs to f that give these

the range of g∘f are the outputs of g , that these give

Answer 14

the domain of g∘f is a subset of the domain of f

the range of g∘f is subset of the range of g

Answer 15

Eh I'm still kind of lost. I'll have to find the textbook and read over that section again. I appreciate the assistance though!

Answer 16

Domain: 2,4,6
Range: 1,2

The domain values pass through and the range values pass through as well.

Answer 17

what if we try g∘f (9) = g( f(9) ) = what does this become?

Answer 18

g(f(9) = 4

Answer 19

f(9) = 4

g( f(9) ) = g(4) =

Answer 20

=1

Answer 21

yes gof(9) = g(f(9)) = 1

the function has passed the value of 9 , so 9 must be in the domain

Answer 22

what if we try g∘f (3) = g( f(3) )
=

Answer 23

=0. There is no value for 3

Answer 24

f(3) = 1

g∘f (3) = g( f(3) )
= g(1)
= does not compute

i.e. 3 is not in the domain of g∘f

Answer 25

Ahh okay I said it wrong. So the domain really comes out to {2,4,8,9} if I'm looking at it correctly now. I was visualizing it incorrectly at first.

Answer 26

thats better , now you've got it!

Answer 27

Can you go over range one more time really quickly? Don't give me the answer but just highlight the most important tips. It helps having an additional explanation sometimes.

Answer 28

The range of g∘f is the subset of the range of g, that can be the result of plugging in elements of that domain into g∘f

Answer 29

e.g. you found g∘f(9) = 1 so 1 is in the range of g∘f

Answer 30

Thanks so much!