$\"\"$

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The functions are $\"\"$ .

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The composition of f with g is $\"\"$

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$\"\"$ (Definition of $\"\"$ )

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$\"\"$ (Definition of $\"\"$ )

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$\"\"$ (Definition of $\"\"$ )

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$\"\"$ (Simplify) $\"\"$

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The composition of g with f is $\"\"$

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$\"\"$ (Definition of $\"\"$ )

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$\"\"$ (Definition of $\"\"$ )

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$\"\"$ (Definition of $\"\"$ )

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$\"\"$ (Simplify)

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Since $\"\"$ .

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Since f and g functions are inverse. $\"\"$

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The functions f and g are inverse.