Question

f(x)=-3-x, g(y)= square root of y+9 g(f(x))= square root of -3-x+9
what is the domain of the function of g(f(x))?

Answer 1

\[g(f(x) = \sqrt{-3-x + 9}...or .....g(f(x) = \sqrt{6 - x}\]

so radicals can't be negative, so for the domain you need to solve

\[6 - x \ge 0\]

and you can always check by picking a value in your domain and testing.

Answer 2

this how my problem looks like
\[f(x)=-3-x, g(y)=\sqrt{y+9} g(f(x))=\sqrt{-3-x+9}\]

Answer 3

Guys. Before you finish anything, the equation is:
\[g(y) = \sqrt{y} + 9\]
I know you said that +9 is included, but then your options would be invalid.

Answer 4

Thanks, now I can unsderstand it.

Question:

\(f(x)=-3-x\)

\(g(y)= \sqrt{y+9} \)

\( g(f(x))= \sqrt{-3-x+9 } \)

What is the domain of the function g(f(x))?

Solution:

g(f(x)) can be simplified to:

\( g(f(x)) = \sqrt{6 - x} \)

Since there is a root in the comopsition, we need to avoid negative values of the radicand.

\(6 - x \ge 0 \)

\(-x \ge -6\)

\(x \le 6\)

This tells you that the domain of the compositiin is all numbers less than or equal to 6.

Answer 5

yeah ur right damn i type too fast that i sometimes make mistakes my bad

Answer 6

a. all real numbers less than or equal to 3
b. all numbers greater than or equal to 3
c. all numbers less than or equal to -3
d. all numbers greater than or equal to -3

Answer 7

yes this are my options

Answer 8

i think its a

Answer 9

None of your choices have the correct answer. Are you sure these are the correct choices for this problem?

Answer 10

yeah

Answer 11

a. all numbers less than or equal to 3
b. all numbers greater than or equal to 3
c. all numbers less than or equal to -3
d. all numbers greater than or equal to -3

Answer 12

DOMAIN:
x ≤ -3
http://www.wolframalpha.com/input/?i= √%28-3-x%29+%2B+9

Answer 13

so c

Answer 14

@romanortiz65

Is

\( g(y) = \sqrt{y} + 9 \)

or

\(g(y) = \sqrt{y + 9} \)

Answer 15

its the first choice u wrote

Answer 16

\[g(y)=\sqrt{y}+9\]

Answer 17

hello anyone there that can still help me

Answer 18

so the answer is C

Answer 19

so its c

Answer 20

so its c

Answer 21

That's not what you wrote above. No wonder my solution didn't match any of the choices.

Answer 22

In your first response after you opened the post, you show (y + 9) inside the square root. Now you are saying only y should be inside the square root.

Answer 23

yeah

Answer 24

a. all numbers less than or equal to 3
b. all numbers greater than or equal to 3
c. all numbers less than or equal to -3
d. all numbers greater than or equal to -3

Answer 25

Yes. Sorry! I wasn't at my computer...