$\"\"$

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The functions is $\"\"$ and inverse function is $\"\"$ .

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(a)

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Find the domain of $\"image\"$ and $\"image\"$ .

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The cubic polynomial function $\"\"$ is increasing function.

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The domain of a function is all possible $\"image\"$ -values.

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Domain of a polynomial function is always all real numbers.

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Domain of $\"image\"$ is $\"\"$ .

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Domain of cube root function is all real numbers.

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Domain of $\"image\"$ is $\"\"$ .

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$\"\"$

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(b)

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Find the range of $\"image\"$ and $\"image\"$ .

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The Domain of $\"image\"$ is equal to the range of $\"image\"$ and the range of $\"image\"$ is equal to the domain of $\"image\"$ .

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Range of $\"image\"$ is $\"\"$ .

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Range of $\"image\"$ is $\"\"$ .

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$\"\"$

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(c)

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Graph the two functions $\"image\"$ and inverse function is $\"\"$ .

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Graph:

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$\"\"$

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$\"\"$

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(d)

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The functions are $\"\"$ and $\"\"$ .

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First derivative is slope of the function.

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Find the slopes of the $\"\"$ and $\"\"$ at the given points.

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$\"\"$

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$\"\"$

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The point is $\"\"$ .

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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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The point is $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The slopes of the $\"image\"$ and $\"image\"$ are reciprocal at the points $\"\"$ , $\"\"$ .

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Graph:

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$\"\"$

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$\"\"$

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(a)

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

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(b)

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Range of $\"image\"$ is $\"image\"$ and range of $\"image\"$ is $\"image\"$ .

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(c)

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$\"\"$

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(d) The slopes of the $\"image\"$ and $\"image\"$ are reciprocal at the points $\"\"$ , $\"\"$ .