# How to find the correct domain for a composite function?

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1. Feb 8, 2017

### AlessandraB34

1. The problem statement, all variables and given/known data
The problem states f(x)= √x-5). When solving for (f)/(f)(x) I got the answer=√(√x-5)
I cannot get the interval notation correct as many times as I input the domain. The square root must of a square root has confused me.

2. Relevant equations
Please view the attached screen shot

3. The attempt at a solution
(-∝,-√5]∪(0,√5]

2. Feb 26, 2018

### scottdave

The square root is more restrictive, do you see why? What is the domain of h(a) = √a ? (what values of a are valid?)
Now what if a = x-5, what are the values that x can be for it to be valid? That is the way that I think about it.

Now try a = x2-5.

3. Feb 26, 2018

### Staff: Mentor

According to your work in the screen shot, $f(x) = \sqrt{x - 5}$.
You should have written f(x) = √(x - 5). It looks like you sort of intended to do this, but omitted the left parenthesis.

4. Mar 2, 2018

### mattt

OK, so $$f(x):=x^2$$ and $$g(x):=\sqrt{x-5}$$

You must undertand that $$x\in Dom(f\circ g)$$ iff $$x\in Dom(g)$$ and $$g(x)\in Dom(f)$$

Obviously $$Dom(f)=\mathbb{R}$$, and $$Dom(g)=[5,+\inf)$$

So what is $$Dom(f\circ g)$$ ?

5. Mar 2, 2018

### Tonyb24

It is f ∘ g.
so basicly, f(g(x)).
So cuz f(x)=x^2, f(g(x))=(g(x)^2.

6. Mar 2, 2018

### Staff: Mentor

No it doesn't, at least if we are to believe your screen shot. In that image, it clearly shows that $f(x) = x^2$.
This notation makes no sense. The problem asks for f(f(x)), among other things.

7. Mar 2, 2018

### Staff: Mentor

Thread closed. For some reason, the OP is not a member here, so won't be able to reply.