Question

what is the domain of the composite function G(F(x))?
given
F(x)=3-x
G(y)=√y
g(F(x))=√3-x

Answer 1

g(f(x)) = sqrt(3 - x)
What values are not allowed inside a square root?

Answer 2

this are the answers to it
x<0
x>3
x≤3
x<3
x≤0
all real numbers

Answer 3

Do you want to understand how to solve this and other similar problems, or you just want the solution?

Answer 4

i want to know how to solve it

Answer 5

Then look above and answer my question.

Answer 6

negatives right?

Answer 7

Good. Inside a square root sign, you can't have negatives. Tha means you can have zero and positive.

Answer 8

Inside the square root symbol, you have 3 - x.
3 - x can be zero or positive. that means you have the inequality
3 - x >= 0

Answer 9

Now you solve that inequality for x to get the answer.

Answer 10

so then you subtract 3 right?

Answer 11

yes

Answer 12

so the answer would be x>3?

Answer 13

3 - x >= 0
-x >= -3
Divide both sides by -1, but remember to change direction of inequality sign:
x <= 3

Answer 14

thats when you divide only by the negative right?

Answer 15

Correct, but it's true if you multiply or divide by a negative number.

Answer 16

ooohh okay i see