Powell Maxwell
11/11/2023 · Elementary School
For \( f(x)=x^{2}+8 \) and \( g(x)=\sqrt{x-3} \), find the following composite functions and state the domain of each. \( \begin{array}{llll}\text { (a) } f \circ g & \text { (b) } g \circ f & \text { (c) } f \circ f & \text { (d) } g \circ g\end{array} \) Select the correct choice below and fill in any answer boxes within your choice. \( \begin{array}{l}\text { (a) }(f \circ g)(x)=x+5 \text { (Simplify your answer.) } \\ \text { (Type domain of } f \circ g \text { is }\{x \mid x \geq 3\} \\ \text { B. The domain of } f \circ g \text { is all real numbers. }\end{array} \) (b) \( (g \circ f)(x)=\square \) (Simplify yost answer.)
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\[
\begin{array}{l}
(g \circ f)(x) = \sqrt{x^2 + 5} \\
\text{定义域:所有实数}
\end{array}
\]
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