Find the domain of the function algebraically and support the answer graphically h times x equal the square root of 4-x squared divided by x - 3

Answer 1

That's h of x, not h times x.

h(x) = √(4-x^2)/(x-3)
or
h(x) = √((4-x^2)/(x-3))

In either case, x=3 is excluded because the denominator is zero.

Now, √z has a domain of z>=0.

In the first case, 4-x^2 >= 0, so x^2 <= 4
|x| <= 2

In the second case, check the domain is (-∞,-2]U[2,3).

See whether you can determine why.