To determine To find for which of the given functions, the value r = 5 a fixed point. Explanation Given: The following equation is given: g ( x ) = 5 + 7 x x + 7 Concept used: If x is a fixed point of a function f(x), then we can write, f ( x ) = x . Calculation: Option (a) The following equation is given: g ( x ) = 5 + 7 x x + 7 To find out whether r = 5 is a fixed-point or not for the given equation g ( x ) = 5 + 7 x x + 7 , let us solve the equation x = g ( x ) . x = g ( x ) x = 5 + 7 x x + 7 Now, x = 5 + 7 x x + 7 x 2 + 7 x = 5 + 7 x x 2 = 5 x = ± 5 So, we can see that r = 5 is a fixed point. Thus, for the equation g ( x ) = 5 + 7 x x + 7 , r = 5 is a fixed point. Option (b) The following equation is given: g ( x ) = 10 3 x + x 3 To find out whether r = 5 is a fixed-point or not for the given equation g ( x ) = 10 3 x + x 3 , let us solve the equation x = g ( x ) . x = g ( x ) x = 10 3 x + x 3 Now, x = 10 3 x + x 3 3 x 2 = 10 + x 2 2 x 2 = 10 x = ± 5 So, we can see that r = 5 is a fixed point. Thus, for the equation g ( x ) = 10 3 x + x 3 , r = 5 is a fixed point

3rd Edition

ISBN: 9780134696454

Author: Sauer, Tim

Publisher: Pearson,

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Chapter 1.2, Problem 6E

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To find for which of the given functions, the value r=5 a fixed point.

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Chapter 1.2, Problem 5E

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