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natita [175]
2 years ago
9

Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plu

s 3 end quantity comma what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
Mathematics
1 answer:
Lostsunrise [7]2 years ago
7 0

The domain of the composite function is given as follows:

[–3, 6) ∪ (6, ∞)

<h3>What is the composite function of f(x) and g(x)?</h3>

The composite function of f(x) and g(x) is given as follows:

(f \circ g)(x) = f(g(x))

In this problem, the functions are:

  • f(x) = \frac{1}{x - 3}.
  • g(x) = \sqrt{x + 3}

The composite function is of the given functions f(x) and g(x) is:

f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}

The square root has to be non-negative, hence the restriction relative to the square root is found as follows:

x + 3 \geq 0

x \geq -3

The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:

\sqrt{x + 3} - 3 \neq 0

\sqrt{x + 3} \neq 3

(\sqrt{x + 3})^2 \neq 3^2

x + 3 \neq 9

x \neq 6

Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:

[–3, 6) ∪ (6, ∞)

More can be learned about composite functions at brainly.com/question/13502804

#SPJ1

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