let's look at it this way:

let

let

then

now h is clearly defined for all x, no problem there.

but g is only defined for x ≥ 0.

that means that f is only defined for h(x) ≥ 0.

so we need to look at what the RANGE of h is, in particular, for which x is h(x) ≥ 0?

this is precisely when:

that is:

.

to see why your answer is wrong, let's pick something in it, and see what happens:

let's use x = -1, which is in the interval (-∞,0].

now x^{2}- 9 = (-1)^{2}- 9 = 1 - 9 = -8. how are we going to take a 4th root of that?

EDIT: darn, i left out an x!

it should be:

x^{2}- 9x (is my memory, or my eyesight, going?)

this is ≥ 0 when either:

x ≥ 0 and x - 9 ≥ 0, that is x ≥ 9...in this case the "9" controls (since its bigger and we have to have both), so this is the interval [x,∞).

or:

x < 0 and x - 9 < 0, that is x < 9...in this case the "0" controls (since it is smaller), so this is the interval (-∞,0].

therefore, the correct answer is as Soroban said:

(-∞,0] U [9,∞).