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

Find the domain of f/g f(x)= sqrt 4-x^2 g(x)= sqrt 3x+4-example-1
User Tsuharesu
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1 Answer

18 votes
18 votes

Answer:

(-4/3, 2]

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]

User Christian Barron
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