What's the interval notation of F(x)=-(square root of) 4-x and g(x)=6-x, this problem's causing me trouble

Question

the answer is [-~, 4) or negative infinity, 4

but how does one go about creating that answer

Answer 1

Note: I hope you didn't mean F(g(x))

for g(x) = 6 - x, x can be any value.
but F(x) = - sqrt(4-x), x cannot be any value.

4 - x must be greater than 0 because sqrt(-number) is not real.

4 - x > 0
- x > - 4
x < 4

which means x can range from -oo (-infinity) to positive 4.

Answer 2

Are you asking for the DOMAIN of F(g(x)) in interval notation??

If so then you have to find the domain of g(x);
which is all real numbers-

Now, take the composite function F(g(x)) as
[Insert g(x) into every value of x in F(x)];

F(g(x))= -square root (4-(6-x)).

The domain is limited by the values of x that cause the square root be of a negative number. So take the determinant (the inside of the square root) and set it equal to 0 to solve for these values.

4 - (6-x) = 0
4 - 6 + x =0
x = 2

Now test x-values on both sides of x =2 to see which values cause the determinant to be negative.

You should get all the values less than 2... thus in interval notation the domain would be all the values excluding these,

[2, infinity)

I hope this helps : )

Answer 3

Based on what you say the answer is, it sounds like you are looking for the domain of F(x). Since you want to avoid taking the square root of a negative number, you need 4-x to always result in a positive number or:

4-x>=0

Solve for x:

-x>= -4

x<=4

This set of numbers can be represented by the interval (- ~, 4]
( negative infinity, 4].

I'm not sure what is going on with g(x) there.

Hope this helps.

Answer 4

f(x) = -(4-x)^.5
(- infinity,4]

g(x) = 6-x.
(-infinity, infinity)
(a,b) means all numbers between a and b
[a,b] means all numbers between a and b including a and b
(a,b] means all numbers between a and b including b