precalculus problem!!!!?

Question

find (f*g)(x) and identify it's domain

f(x)= sqrt (x+8) ; g(x)=1-x^2

Answer 1

Is (f*g)(x) the same as f[g(x)]?

If it is, then it is sqrt [9 - (x^2)].

f[g(x)] = sqrt [g(x) + 8] = sqrt [ 1 - (x^2) + 8] = sqrt [9 - (x^2)]

If you set that to 0, then x would be -3 or +3...

Answer 2

don't listen to them

(f*g)(x) = f(x)g(x)
(f°g)(x) = f(g(x))

f(x) = sqrt(x + 8)
g(x) = 1 - x^2

(f*g)(x) =
(1 - x^2)sqrt(x + 8) =
sqrt((1 - x^2)^2 * (x + 8)) =

1 - x^2 = 0
-x^2 = -1
x^2 = 1
x = -1 or 1

the domains are
-8 < x < -1
-1 < x < 1
1 < x < ∞

Answer 3

f[g(x)] = f[1 - x²] = √[(1 - x²) + 8] = √(9 - x²)

The domain is -3 ≤ x ≤ 3.