$\"\"$

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The function is $\"\"$ and the inverse function is $\"\"$ , $\"\"$ .

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(a)

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

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The function is $\"\"$ , $\"\"$ .

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

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

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The inverse function is $\"\"$ .

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The denominator of the fraction should not be zero.

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Fraction under the square root is always positive.

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$\"\"$ and $\"\"$

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$\"\"$ and $\"\"$

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$\"\"$ .

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The function is defined for $\"\"$ .

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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 :

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Graph the functions $\"\"$ and $\"\"$ .

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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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Slope of the function is the first derivative of the function.

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"image\"$ .

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$\"\"$

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$\"\"$ .

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Find slope at the point $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"image\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Find slope at the point $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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(a)

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

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

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(b)

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

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

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(c)

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Graph :

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Graph the functions $\"\"$ and $\"\"$ .

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$\"\"$

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(d)

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