Question

If f(x)=2-x^1/2 and g(x)=x^2-9 , what is the domain of g(x)÷f(x)

A)(- ∞,2) and (2, ∞)
B) (0,4) and (4, ∞)
C)(- ∞,2) and (4, ∞)
D)(- ∞,-2) and (2, ∞)

Answer 1

First let P(x) = g(x)/f(x) = x^2 - 9 / 2 - x^0.5


The domain of the nominator is any value

The domain of the denominator is

Zeros of the denominator

2-x^0.5 = 0

-x^0.5 = -2

x^0.5 = 2

x = 4

domain of x^0.5 is x >= 0

(0,4) and (4, inf)