$\"\"$

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(a)

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Graph of the function $\"\"$ is given.

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Observe the graph, no horizontal line touches the graph of the curve more than once.

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Therefore, $\"\"$ is a one-to-one function by horizontal line test.

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$\"\"$

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(b)

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Find domain and range of $\"\"$ :

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Observe the graph,

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Domain of the function $\"\"$ is $\"\"$ .

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Range of the function $\"\"$ is $\"\"$ .

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Domain of $\"\"$ is range of $\"\"$ and range of $\"\"$ is domain of $\"\"$ .

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Therefore, Domain of $\"\"$ is $\"\"$ and range of $\"\"$ is $\"\"$ .

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$\"\"$

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(c)

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Find $\"\"$ .

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Observe the graph, $\"\"$ .

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From the inverse function definition, if $\"\"$ then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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$\"\"$ .

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$\"\"$

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(d)

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Find $\"\"$ .

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Observe the graph, $\"\"$ .

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From the inverse function definition, if $\"\"$ then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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$\"\"$ .

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$\"\"$

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(a) The function $\"\"$ is a one-to-one function by horizontal line test.

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(b) Domain of $\"\"$ is $\"\"$ and range of $\"\"$ is $\"\"$ .

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(c) $\"\"$ .

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(d) $\"\"$ .