# Domain of a composite function

1. Oct 14, 2014

### ilii

1. The problem statement, all variables and given/known data
Given the Functions
f(x)=4x-1
g(x)=3-2x^2
h(x)= sqrt (x+5)

What is the domain of h(g(x))?
2. Relevant equations

the subject is finding the domain of a composite function
3. The attempt at a solution
I don't understand what I have to 'bring over' from g(x). I think x cannot equal zero for g(x). If someone could post a structured list of steps I need to take to find the domain of a composite function, it would be much appreciated.

thank you

2. Oct 15, 2014

### ShayanJ

The domain of a composite function $(f \circ g)(x)=f(g(x))$ is defined as $D(f\circ g)=\{x \epsilon D(g) | g(x) \epsilon D(f) \}$. So you should find the domains of f and g and check that for what subset of the domain of g, it gives values in the domain of f.

3. Oct 15, 2014

### LCKurtz

Why do you think that? $g(x)$ is just a polynomial. What' wrong with $g(0)$?
What is the formula for $h(g(x))$? What values of $x$ work in that?

4. Oct 15, 2014

### HallsofIvy

The domain of square root is "numbers greater than or equal to 0". h(x)= sqrt(x- 5) so the domain of h is "$x- 5\ge 0$ or $x\ge 5$. That means that $g(x)= 3- 2x^2$ must give only values greater than or equal to 5. Can you solve $3- 2x^2\ge 5$?

Last edited by a moderator: Oct 16, 2014
5. Oct 15, 2014

### ilii

thanks everyone I understand it much better now :D