Provide an Appropriate Response $\mathrm { f } ( \mathrm { x } ) = \sqrt { 9 - \mathrm { x } ^ { 2 } } , 0 \leq \mathrm { x } \leq 1$

question 86

Multiple Choice

Provide an appropriate response.
-Consider the graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt { 9 - \mathrm { x } ^ { 2 } } , 0 \leq \mathrm { x } \leq 1$ . What symmetry does the graph have? Is $\mathrm { f }$ its own inverse?

• A) The graph of \(\mathrm { f }\) has no symmetry. The function \(\mathrm { f }\) is not its own inverse because there is no symmetry.
• B) The graph of \(\mathrm { f }\) is symmetric with respect to the \(\mathrm { y }\)-axis. The function \(\mathrm { f }\) is not its own inverse because \(( f \circ f ) ( x ) = | x |\).
• C) The graph of \(\mathrm { f }\) is symmetric with respect to the \(y\)-axis. The function \(\mathrm { f }\) is its own inverse because (f \(\circ f ) ( x ) = x\).
• D) The graph of \(\mathrm { f }\) is symmetric with respect to the line \(\mathrm { y } = \mathrm { x }\). The function \(\mathrm { f }\) is its own inverse because (f of \() ( x ) = x\).

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