(a)

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Step 1:

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The function is $\"\"$ .

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Rewrite the function as an equation relating $\"\"$ and $\"\"$ .

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$\"\"$

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Exchange $\"\"$ and $\"\"$ in the equation.

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$\"\"$

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Solve the equation for $\"\"$ .

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$\"\"$

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Replace $\"\"$ with $\"\"$ .

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$\"\"$

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

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The graph of $\"\"$ is the reflection of the graph of $\"\"$ in the line $\"\"$ .

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Solution:

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The inverse function is $\"\"$ .

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(b)

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Step 1:

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

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Find the Composition of functions.

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Find $\"\"$ .

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Composition of functions formula: $\"\"$

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Substitute $\"\"$ in the formula.

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$\"\"$

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Substitute again $\"\"$ in $\"\"$ and simplify.

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$\"\"$

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$\"\"$

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Find $\"\"$ .

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Composition of functions formula: $\"\"$ .

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Substitute $\"\"$ in the formula.

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$\"\"$

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Substitute again $\"\"$ in $\"\"$ and simplify.

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$\"\"$

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$\"\"$

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Therefore, $\"\"$

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Solution:

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The functions $\"\"$ and $\"\"$ are inverses of each other. \ \ \ \ (c) \ \

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From a:

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Consider the functions are $\"\"$ and $\"\"$ .

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

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$\"\"$

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Observe the graph:

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Since, the graph of $\"\"$ is the reflection of the graph of $\"\"$ in the line $\"\"$ .

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The functions $\"\"$ and $\"\"$ are inverses of each other.