- $$ f(x)=\sqrt{2 x+4} \quad g(x)=\sqrt{2 x+4} $$

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Both functions $$ f(x) $$ and $$ g(x) $$ have a domain of $$ [-2, \infty) $$ and a range of $$ [0, \infty) $$. It looks like you have two functions defined as follows: $$ f(x) = \sqrt{2x + 4} $$ $$ g(x) = \sqrt{2x + 4} $$ Since both functions are identical, we can analyze them together. ### Domain To find the domain of $$ f(x) $$ and $$ g(x) $$, we need to ensure that the expression inside the square root is non-negative: $$ 2x + 4 \geq 0 $$ Solving this inequality: $$ 2x \geq -4 \ x \geq -2 $$ Thus, the domain of both functions is: $$ [-2, \infty) $$ ### Range Next, we can find the range of the functions. The minimum value occurs when $$ x = -2 $$: $$ f(-2) = \sqrt{2(-2) + 4} = \sqrt{0} = 0 $$ As $$ x $$ increases, $$ f(x) $$ and $$ g(x) $$ will also increase without bound. Therefore, the range of both functions is: $$ [0, \infty) $$ ### Summary - **Domain**: $$ [-2, \infty) $$ - **Range**: $$ [0, \infty) $$ If you have any specific operations or questions regarding these functions, feel free to ask!

- \( f(x)=\sqrt{2 x+4} \quad g(x)=\sqrt{2 x+4} \)

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- \( f(x)=\sqrt{2 x+4} \quad g(x)=\sqrt{2 x+4} \)

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