true or false
when you compose two functions. the domain and range of the original functions does not influence the domain and range of their composition

Question

true or false 
when you compose two functions. the domain and range of the original functions does not  influence the domain and range of their composition

anonymous · Answer

i think its true

mathstudent55 · Answer

I think the domain and range of the original function DO influence the domain and range of the composition. The answer is false.

anonymous · Answer

damn okay man

anonymous · Answer

$$F(X)=-3-X,G(Y)=\sqrt{Y+9} G(F(X))=\sqrt{-3-X+9}$$

mathstudent55 · Answer

$f(x)=-3-x$

$g(y)=\sqrt{y+9}$

$g(f(x))=\sqrt{-3-x+9} $

$g(f(x) = \sqrt{6 - x} $

Ok, now we have g(f(x)), now what is the question?

anonymous · Answer

would it be all number less than or equal to 3

mathstudent55 · Answer

No.
You need to look at the compositioin and see what there is in it that can cause a problem in the domain. There is a square root in the composition. The radicand cannot be negative.

The domain of the composition is all values of x that will not make the radicand negative.

We need to solve this inequality:

$ 6 - x \ge 0$

$-x \ge -6$

$x \le 6$

This is the domain.

anonymous · Answer

do you have to divide the 6

mathstudent55 · Answer

In the final answer? No.

$x \le 6$ is the final answer for the domain.
In other words, the domain is all real numbers equal to or less than 6.

anonymous · Answer

Hello again! Sorry, I had to shut off my computer... but @mathstudent55 has got it all!

anonymous · Answer

i think you did something wrong because my choices are 
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

mathstudent55 · Answer

I have a better idea. Why don't you start a problem by statinmg whant we are looking for? You started this problem in the middle of a post about anouther problem and then you stated what function f, function g and their composition were. You never even asked what the question was. Start a new post and be clear as to what your asking. Copy the problem exaclty as you see it instead of having us wasting our time answering what we think the question is but not ever being sure.

anonymous · Answer

The equation is probably... $$g(y) = \sqrt{y} + 9$$