For the real-valued functions $f (x) = x^{2} - 1$ and $g (x) = \sqrt{x + 4}$ , find the composition $f \circ g$ and specify its domain using interval notation
$\begin{array}{l} (f \circ g) (x) = ◻ \\ Domain of f \circ g : ◻ \end{array}$

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$Domain of f \circ g : [- 4, \infty)$

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Step 1 ： $f (g (x)) = (\sqrt{x + 4})^{2} - 1$

Step 2 ： $f (g (x)) = x + 4 - 1 = x + 3$

Step 3 ： $g (x) = \sqrt{x + 4}$ is defined for all $x$ such that $x + 4 \geq 0$ , so $x \geq - 4$

Step 4 ： $f (g (x)) = x + 3$ is defined for all real numbers. However, since $g (x)$ is part of the composition, we must also consider the domain of $g (x)$ . Therefore, the domain of $f \circ g$ is all $x$ such that $x \geq - 4$

Step 5 ： $(f \circ g) (x) = x + 3$

Step 6 ： $Domain of f \circ g : [- 4, \infty)$

For the real-valued functions f(x)=x2−1 and g(x)=x+4, find the composition f∘g and specify its domain using interval notation(f∘g)(x)=◻ Domain of f∘g:◻

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For the real-valued functions $f (x) = x^{2} - 1$ and $g (x) = \sqrt{x + 4}$ , find the composition $f \circ g$ and specify its domain using interval notation
$\begin{array}{l} (f \circ g) (x) = ◻ \\ Domain of f \circ g : ◻ \end{array}$