$\"\"$

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(a)

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The function is $\"\"$ .

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Show that the function is and odd function.

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When the function is an odd function then $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Hence, $\"\"$

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Threrefore, the function $\"\"$ is an odd function.

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$\"\"$

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(b)

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Find the inverse function of $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Take squareroot on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Interchange $\"\"$ and $\"\"$ .

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$\"\"$

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Hence, $\"\"$

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Therefore, the inverse function is $\"\"$ .

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$\"\"$

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(a) The function $\"\"$ is an odd function.

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(b) The inverse function of $\"\"$ is $\"\"$ .