Explanation Given information: g is the inverse of f Formula used: f ( f − 1 ( x ) ) = x ; f − 1 ( f ( x ) ) = x Calculation: In general, Let f ( x ) be a function, inverse f − 1 ( x ) exists then f ( f − 1 ( x ) ) = x ; f − 1 ( f ( x ) ) = x (a) Consider the function f ( x ) + 1 Consider g ( x ) / 4 From the general statement f ( g ( x ) / 4 ) + 1 ≠ x Thus, g ( x ) / 4 is not an inverse of f ( x ) + 1 . Next consider g ( x / 4 ) f ( g ( x / 4 ) ) + 1 ≠ x Thus, g ( x / 4 ) is not an inverse of f ( x ) + 1 . Next consider g ( x − 1 ) f ( g ( x − 1 ) ) + 1 = x − 1 + 1 Since f ( g ( x ) ) = x And g ( g ( x ) + 1 − 1 ) = g ( f ( x ) ) Since g ( f ( x ) ) = x Thus, g ( x − 1 ) is an inverse of f ( x ) + 1 . Therefore, the inverse of the function ( a ) is ( iii ) (b) Consider the function f ( x + 1 ) . Consider g ( x ) / 4 From the general statement, f ( g ( x ) / 4 + 1 ) ≠ x Thus, g ( x ) / 4 is not an inverse of f ( x + 1 ) . Next consider g ( x / 4 ) f ( g ( x / 4 ) + 1 ) ≠ x Thus, g ( x / 4 ) is not an inverse of f ( x + 1 )

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

4th Edition

ISBN: 9781319411657

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1, Problem 65CRE

To determine

Match the functions (a)−(d) With their inverses (i)−(iv).

(a) f(x)+1 (b) f(x+1) (c) 4f(x) (d) f(4x)(i) g(x)/4 (ii) g(x/4) (iii) g(x−1) (iv) g(x)−1

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Chapter 1, Problem 64CRE

Chapter 1, Problem 66CRE

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Chapter 1 Solutions

ACHIEVE FOR CALCULUS 1 TERM >CSI CUSTOM<

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Match the functions ( a ) − ( d ) With their inverses ( i ) − ( iv ) . ( a ) f ( x ) + 1 ( b ) f ( x + 1 ) ( c ) 4 f ( x ) ( d ) f ( 4 x ) ( i ) g ( x ) / 4 ( ii ) g ( x / 4 ) ( iii ) g ( x − 1 ) ( iv ) g ( x ) − 1

Solution Summary: The author explains how to match functions with their inverses.

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Match the functions (a)−(d) With their inverses (i)−(iv).

(a) f(x)+1 (b) f(x+1) (c) 4f(x) (d) f(4x)(i) g(x)/4 (ii) g(x/4) (iii) g(x−1) (iv) g(x)−1

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Chapter 1 Solutions

Match the functions ( a ) − ( d ) With their inverses ( i ) − ( iv ) . ( a ) f ( x ) + 1 ( b ) f ( x + 1 ) ( c ) 4 f ( x ) ( d ) f ( 4 x ) ( i ) g ( x ) / 4 ( ii ) g ( x / 4 ) ( iii ) g ( x − 1 ) ( iv ) g ( x ) − 1

Solution Summary: The author explains how to match functions with their inverses.

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Match the functions (a)−(d) With their inverses (i)−(iv). (a) f(x)+1 (b) f(x+1) (c) 4f(x) (d) f(4x)(i) g(x)/4 (ii) g(x/4) (iii) g(x−1) (iv) g(x)−1

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Chapter 1 Solutions

Match the functions (a)−(d) With their inverses (i)−(iv).

(a) f(x)+1 (b) f(x+1) (c) 4f(x) (d) f(4x)(i) g(x)/4 (ii) g(x/4) (iii) g(x−1) (iv) g(x)−1