# Finding the domain of a composite function help.

1. Sep 17, 2012

### nukeman

1. The problem statement, all variables and given/known data

Ok, I just worked out a composite function, and it left me with:

√2x^2+5)

Now, how do I find the domain from that? I don't understand that my text says the domain of that is just all Real numbers ???

What makes this different than other square functions that we are able to find the domain like: √2-x ?

2. Relevant equations

3. The attempt at a solution

2. Sep 17, 2012

### Villyer

This isn't any different from those. How would you go about finding the domain of the example function you posted?

3. Sep 17, 2012

### nukeman

Then why did my book say the domain is all REAL numbers?

I would go:

4. Sep 18, 2012

### Staff: Mentor

You did a bunch of work that doesn't get you anywhere.

The square of any real number is ≥ 0.

IOW, x2 ≥ 0, for all real x
so 2x2 ≥ 0, for all real x
so 2x2 + 5 ≥ 5, for all real x

5. Sep 18, 2012

### nukeman

Kinda lost here.

So, 2x^2 + 5

the 2x^2 part is always the same, as 2x^2, x can be any real number. And why is that?

how did you get 2x^2 + 5 <= 5?

What would the domain be?

Thanks Mark!!

6. Sep 18, 2012

### Saitama

x2 is always positive, do you expect 2x2 or 2x2+5 to result a negative number?
x can be any real number because square of every real number is defined.

7. Sep 18, 2012

### nukeman

Oh....ok

So, everytime I get a 2x^2 in a square root, and have to find the domain, its just all real numbers? Then I just worry about what after it, like the +5?

But then, wouldnt 2x^2 + 5 be x >= -5?

8. Sep 18, 2012

### Staff: Mentor

This is not a complete statement. So 2x2 + 5 is what?
I didn't. I got 2x2 + 5 ≥ 5
If you have an expression like x2, or 2x2 or .1x2, it is always guaranteed to be ≥ 0, because the square of any real number can't be negative.
NO!

2x2 + 5 is an expression that has a value for each value of x.

x ≥ -5,
2x2 + 5 = 0,
2x2 + 5 < 0,
and
2x2 + 5 ≥ 0
are all statements that are either true or false, possibly depending on the value of x, but possibly not.

You can't compare 2x2 + 5 (an expression) and x ≥ -5 (a statement).

If you start with this statement:
2x2 + 5 ≥ 0,

you can add -5 to both sides to get
2x2 ≥ -5

This is legitimate, but unwise. Since x2 ≥ 0 for all real x, then 2x2 ≥ 0 for all x, so 2x2 is automatically ≥ -5.

9. Sep 18, 2012

### nukeman

Oh ok, I see what you mean here. Thanks Mark.

So, for that expression, if they ask for the domain of that expression, what would it be? That is where I am lost.

10. Sep 18, 2012

### Staff: Mentor

By that expression, I assume you mean $\sqrt{2x^2 + 5}$, right? I don't see how you can still be asking this. You know the answer, and this thread has explained what's going on in considerable detail.

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