# Thread: Find the following functions and their domains

1. ## Find the following functions and their domains

Find each of the following functions and state their domains.

F(x) = (x-5)^.5

and

G(x) = (x^2 -4)^.5

2. ## Re: Find the following functions and their domains

Originally Posted by TenaciousE
Find each of the following functions and state their domains.

F(x) = (x-5)^.5

and

G(x) = (x^2 -4)^.5
$\displaystyle f(x) = \sqrt{x-5}$ ... $\displaystyle x - 5 \ge 0$ (why?) ... $\displaystyle x \ge 5$

3. ## Re: Find the following functions and their domains

What do you mean by "find the functions"? They are pretty much right there aren't they?
As for the domains, both of those are square roots. Which numbers can you take the square root of which can you not? I assume we are talking about real numbers.

4. ## Re: Find the following functions and their domains

Oops I left out the last part of the question xD

Find the functions for:

f + g,
f - g,
fg, and
f/g

And we have to find the domains of the new functions that we are finding

5. ## Re: Find the following functions and their domains

Originally Posted by skeeter
$\displaystyle f(x) = \sqrt{x-5}$ ... $\displaystyle x - 5 \ge 0$ (why?) ... $\displaystyle x \ge 5$

I've given you the domain of f (you still need to tell me why), but my other question still stands ... what about the domain of g(x)?

you're going to need that information to find the domain of f + g, f - g, fg, and f/g

6. ## Re: Find the following functions and their domains

I know how to find the domains of the individual functions. I don't know how to combine the radicals and find the domain of that resulting function.

To answer your question, the domain for f is x is less than or equal to 5 because any value for x greater than 5 would put a negative under the radical. For the same reason, the domain for g would be x is all real numbers excluding 2 and -2

7. ## Re: Find the following functions and their domains

Originally Posted by TenaciousE
I know how to find the domains of the individual functions. I don't know how to combine the radicals and find the domain of that resulting function.

To answer your question, the domain for f is x is less than or equal to 5 because any value for x greater than 5 would put a negative under the radical. For the same reason, the domain for g would be x is all real numbers excluding 2 and -2
you have this backwards ... the domain of f is x is greater than or equal to 5

and , this is totally wrong.

for g(x) , the value of $\displaystyle x^2-4$ must be greater than or equal to 0 ... for what interval(s) of x is that true?

8. ## Re: Find the following functions and their domains

that would be from (-inf, -2] U [2, inf), correct?

9. ## Re: Find the following functions and their domains

Originally Posted by TenaciousE
that would be from (-inf, -2] U [2, inf), correct?
that would be the domain of g(x)