Explanation Given: The given functions are f ( x ) = x 2 and g ( x ) = x + 1 . Concept used: Substitution of a for x in a function f ( x ) and g ( x ) will give the value of f ( a ) and g ( a ) . Take the value of g ( a ) as a and put it in the function f ( x ) to get the value of f ( g ( a ) ) . Calculation: Let us consider the functions f ( x ) = x 2 and g ( x ) = x + 1 To determine (b) To find the value of g ( f ( 1 ) ) . To determine (c) To find the function f ( g ( x ) ) . To determine (d) To find the function g ( f ( x ) ) . To determine (e) To find the value of f ( t ) ⋅ g ( t ) .

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 1.8, Problem 7P

To determine

(a)

To find the value of f(g(1)).

To determine

(b)

To find the value of g(f(1)).

To determine

(c)

To find the function f(g(x)).

To determine

(d)

To find the function g(f(x)).

To determine

(e)

To find the value of f(t)⋅g(t).

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Chapter 1.8, Problem 6P

Chapter 1.8, Problem 8P

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4 Consider f(x) periodic function with period 2, coinciding with (x) = -x on the interval [,0) and being the null function on the interval [0,7). The Fourier series of f: (A) does not converge in quadratic norm to f(x) on [−π,π] (B) is pointwise convergent to f(x) for every x = R П (C) is in the form - 4 ∞ +Σ ak cos(kx) + bk sin(kx), ak ‡0, bk ‡0 k=1 (D) is in the form ak cos(kx) + bk sin(kx), ak 0, bk 0 k=1

Chapter 1 Solutions

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(a) To find the value of f ( g ( 1 ) ) .

Solution Summary: The author explains how to find the value of f(g(1)).

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(a)

To find the value of f(g(1)).

(b)

To find the value of g(f(1)).

(c)

To find the function f(g(x)).

(d)

To find the function g(f(x)).

(e)

To find the value of f(t)⋅g(t).

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(a) To find the value of f ( g ( 1 ) ) .

Solution Summary: The author explains how to find the value of f(g(1)).

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(a) To find the value of f(g(1)).

(b) To find the value of g(f(1)).

(c) To find the function f(g(x)).

(d) To find the function g(f(x)).

(e) To find the value of f(t)⋅g(t).

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Chapter 1 Solutions

(a)

To find the value of f(g(1)).

(b)

To find the value of g(f(1)).

(c)

To find the function f(g(x)).

(d)

To find the function g(f(x)).

(e)

To find the value of f(t)⋅g(t).