$\"\"$

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The function is $\"\"$ .

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Horizontal line test:

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A function $\"\"$ has an inverse $\"\"$ if and only if no horizontal line intersects its graph of the function at most one point.

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Graph :

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Graph the function $\"\"$ .

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Draw the horizontal line $\"\"$ .

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$\"\"$

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Observe the graph:

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The horizontal line $\"\"$ touches the graph of the function only one point.

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The function is an one-to-one, because it passes the horizontal line test.

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Therefore the inverse of the function exist.

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$\"\"$

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To find the inverse of the function, consider $\"\"$ and solve $\"\"$ in terms of $\"\"$ .

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$\"\"$

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$\"\"$

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Square on both sides.

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$\"\"$

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$\"\"$

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Now interchange $\"\"$ as $\"\"$ and $\"\"$ as $\"\"$ .

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$\"\"$

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$\"\"$

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

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$\"\"$

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Find the domain of $\"\"$ .

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The function under the square root should not be negative.

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$\"\"$

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$\"\"$ .

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Domain of the function $\"\"$ is $\"\"$ .

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

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Find the domain of $\"\"$ .

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$\"\"$ is defined for all values of $\"\"$ .

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The domain of the function $\"\"$ is all real numbers i.e $\"\"$ .

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Restrictions over the domain of $\"\"$ :

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The domain of inverse function $\"\"$ is the range of the function $\"\"$ .

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

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Hence the domain of $\"\"$ is $\"\"$ .

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$\"\"$

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

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