Explanation Given: The composite function is R ( x ) = x − 1 . Calculation: Name the expression x as h ( x ) = x . Thus, R ( x ) = h ( x ) − 1 . Replace h ( x ) by x to obtain the expression for g ( x ) . Therefore, R ( x ) = x − 1 . Name the expression x − 1 as g ( x ) = x − 1 . Thus, R ( x ) = g ( x ) Similarly, replace g ( x ) by x to obtain the expression for f ( x ) . Therefore, f ( x ) = x . Hence, it can be concluded that R ( x ) = x − 1 can be expressed as R ( x ) = f ( g ( h ( x ) ) ) , where f ( x ) = x , g ( x ) = x − 1 and h ( x ) = x . Verification: The composite function ( f ∘ g ∘ h ) ( x ) is defined as follows. ( f ∘ g ∘ h ) ( x ) = f ( g ∘ h ) ( x ) First find the composite function of ( g ∘ h ) ( x )

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Author: Stewart

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Chapter 1.3, Problem 49E

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To express: The function R(x)=x−1 in the form of (f∘g∘h)(x) .

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Chapter 1.3, Problem 48E

Chapter 1.3, Problem 50E

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To express: The function R ( x ) = x − 1 in the form of ( f ∘ g ∘ h ) ( x ) .

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To express: The function R(x)=x−1 in the form of (f∘g∘h)(x) .

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