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9. Show that the following functions are their own inverses. (a) The function f: (0, 0) (0,00) given by f(x) = 1/x. (b) The function : P(S)→ P(S) defined by (A) = A *. (c) The function g: R → R given by g(x)=1-x.

9. Show that the following functions are their own inverses. (a) The function f: (0, 0) (0,00) given by f(x) = 1/x. (b) The function : P(S)→ P(S) defined by (A) = A *. (c) The function g: R → R given by g(x)=1-x.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9. Show that the following functions are their own inverses. (a) The function f: (0,00)→→ (0,00) given by f(x)=1/x. (b) The function : P(S)→ P(S) defined by $(A) = A *. (c) The function g: R→ R given by g(x) = 1-x.
Transcribed Image Text:9. Show that the following functions are their own inverses. (a) The function f: (0,00)→→ (0,00) given by f(x)=1/x. (b) The function : P(S)→ P(S) defined by $(A) = A *. (c) The function g: R→ R given by g(x) = 1-x.
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Step 1

Introduction:

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

The output of a function is returned by the inverse function, which also returns the initial value.

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