Question

Find the domain of f/g f(x)= sqrt 4-x^2 g(x)= sqrt 3x+4

Answer 1

Answer:

(-4/3, 2]

Step-by-step explanation:

f(x)= sqrt (4-x^2)

g(x) = sqrt (3x+4)

domain of f(x)/ g(x)

The domain of the numerator is

4-x^2 ≥ 0

4 ≥x^2

Taking the square root of each side

-2 ≤x≤2

The domain of the denominator

3x+4 > 0  ( the denominator cannot be zero)

3x>-4

x > -4/3

Combine the restrictions to make it most restrictive

-4/3<x≤2

In interval notation

(-4/3, 2]