$\"\"$

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The function is $\"\"$

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f is increasing over its entire domain, $\"\"$ . To verify this, note that $\"\"$ is positive on the domain of f. So, f is strictly monotonic and it must have an inverse function. To find an equation for the inverse function, let y = f(x) and solve for x in terms of y.

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$\"\"$ (Let y = f(x))

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$\"\"$ (Divide each side by 3)

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$\"\"$ (Interchange x and y)

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$\"\"$ (Replace y by $\"\"$ )

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$\"\"$

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The domain of $\"\"$ is the range of f, which is $\"\"$ you can verify this results as shown.

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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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Ggaphically

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$\"\"$

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$\"\"$

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Therefore Domain of f and $\"\"$ : all real numbers.

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Range of f and $\"\"$ : all real numbers.