$\"\"$

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The functions is $\"\"$ .

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(a)

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Find an equation for the inverse of function $\"\"$ .

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Consider $\"\"$ and solve for $\"\"$ in terms of $\"\"$ .

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$\"\"$

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Square roots on both sides.

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$\"\"$

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$\"\"$

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Take out the common term $\"\"$ .

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$\"\"$

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$\"\"$ , for $\"\"$ .

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

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$\"\"$

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Replace $\"\"$ by $\"\"$ .

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$\"\"$ , $\"\"$ .

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$\"\"$

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(b)

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Graph :

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

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$\"\"$

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Observe the graph,

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The two functions are symmetrical about the line $\"\"$ .

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$\"\"$ and $\"\"$ are inverse functions.

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$\"\"$

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(c)

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Find the relation between the graphs of the function and its inverse.

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Find $\"\"$ .

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$\"\"$

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$\"\"$

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Find $\"\"$ .

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$\"\"$

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$\"\"$

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The composite function $\"\"$ and $\"\"$ .

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The inverse of function is $\"\"$ .

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Therefore function $\"\"$ and $\"\"$ are symmetric with respect to $\"\"$ .

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$\"\"$

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(d)

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

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Domain is the set of values of $\"\"$ which makes the function mathematically correct.

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Domain of $\"\"$ is set of all real numbers.

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The domain of $\"\"$ is $\"\"$ .

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Range is the output values of the function.

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Range of the $\"\"$ is $\"\"$ .

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Range of $\"\"$ is set of all real numbers.

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$\"\"$

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(a)The inverse function of f is $\"\"$ .

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(b) Graph :

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

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$\"\"$

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Observe the graph,

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The two functions are symmetrical about the line $\"\"$ .

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$\"\"$ and $\"\"$ are inverse functions.

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(c) The function $\"\"$ and $\"\"$ are symmetric with respect to $\"\"$ .

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(d)

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Domain of $\"\"$ is set of all real numbers and the domain of $\"\"$ is $\"\"$ .

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Range of the $\"\"$ is $\"\"$ and Range of $\"\"$ is set of all real numbers.