Find the domain of this
becuase its to the 4th root we have a restirction unlike an odd root which is all real number
why am I wrong ?
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,∞).