About domain and ranges: g(x) = sqrt[-x], h(x) = {x - 1} + 2

[georgebaseball]

Please help me to find the domains and ranges of the following functions:

1) g(x) = √ -x

2) h(x) = {x - 1} + 2

3) f(x) √x + 4 + 3

Thank you!

 

[stapel]

The domain is all allowable x-values. So check functions for problem values, and then the domain is everything else. For instance, you would want to discard any x-values that would cause division by zero or a negative inside a square root.

The range is all resulting y-values. In algebra, this is usually found by looking at the graph.

1) g(x) = sqrt[-x]: What can you not have inside a square root?

2) What is the meaning of the grouping symbols? (Curly braces usually mean the same thing, in this context, as parentheses, but that wouldn't appear to make sense here.)

3) Is the function "f(x) = sqrt[x + 4] + 3", or something else?

Thank you.

Eliz.

 

[georgebaseball]

again thanks for your help, stapel

1) g(x) = √ -x so here the domain and the range is any number < than 1
2) h(x) = {x - 1} + 2 here I had posted wrongly those grouping symbols, this is how it is

h(x) = |x - 1 |+ 2 so the domain is the natural numbers? and the range is any number > 2

3) f(x) √x + 4 + 3 as you said this is the function f(x) = sqrt[x + 4] + 3 so the domain I think would be the rational numbers and the range would be > than 3


please correct me
thanks stapel.

 

[Mrspi]

again thanks for your help, stapel

1) g(x) = √ -x so here the domain and the range is any number < than 1
2) h(x) = {x - 1} + 2 here I had posted wrongly those grouping symbols, this is how it is

h(x) = |x - 1 |+ 2 so the domain is the natural numbers? and the range is any number > 2

3) f(x) √x + 4 + 3 as you said this is the function f(x) = sqrt[x + 4] + 3 so the domain I think would be the rational numbers and the range would be > than 3


please correct me
thanks stapel.

Well, I'm not stapel.....but here goes.

1) g(x) = √ (-x)

What is under the radical sign must be greater than or equal to 0. So,
-x > 0
Multiply both sides of the inequality by -1; remember that you need to reverse the direction of the inequality symbol when you multiply by a negative:

-1(-x) < -1(0)
x < 0

So, the domain is all real numbers less than or equal to 0.

Now, what about the range? The square root of any non-negative real number is a non-negative real number. So, the range is all real numbers greater than or equal to 0.

2) h(x) = | x - 1 | + 2

You could use any real number for x, since it is possible to take the absolute value of anything. Domain is all real numbers.

Now, regardless of what you use for x, | x - 1 | will be greater than or equal to 0. So, h(x) > 2 and the range is all real numbers greater than or equal to 2.

3) f(x) = √(x + 4) + 3

As in problem 1, we must recognize that the quantity under the radical sign must be greater than or equal to 0:

x + 4 > 0
x > -4
The domain is all real numbers greater than or equal to -4.

You have the correct range.

I do not understand why you are restricting domains to things like "rational numbers" or "natural numbers." Perhaps there is something in your instructions that you didn't tell us??

 

[georgebaseball]

Thanks Mrspi , now I really understand a lot better
and was putting natural and rational numbers as the domains because I wasn't sure how it was done.