Math, asked by abhinavpp24, 10 months ago

Let f : W → W be defined as f (n) = n – 1, if n is odd and f (n) = n + 1, if n is even. Show that f is invertible. Find the inverse of f. Here, W is the set of all whole numbers.

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Answered by mayajakhar79

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$<!DOCTYPE html><html lang="en"><head><meta charset="UTF-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Arc reacter</title><link rel="stylesheet" href="design.css" /></head><body><div class="fullpage-wrapper"> <div class="reactor-container"> <div class="reactor-container-inner circle abs-center"></div> <div class="tunnel circle abs-center"></div> <div class="core-wrapper circle abs-center"></div> <div class="core-outer circle abs-center"></div> <div class="core-inner circle abs-center"></div> <div class="coil-container"> <div class="coil coil-1"></div> <div class="coil coil-2"></div> <div class="coil coil-3"></div> <div class="coil coil-4"></div> <div class="coil coil-5"></div> <div class="coil coil-6"></div> <div class="coil coil-7"></div> <div class="coil coil-8"></div> </div> </div> </div><style>body {margin: 0;}.fullpage-wrapper {width: 100%;height: 100vh;background: radial-gradient(#353c44, #222931);display: flex;}.reactor-container {width: 300px;height: 300px;margin: auto;border: 1px dashed #888;position: relative;border-radius: 50%;background-color: #384c50;border: 1px solid rgb(18, 20, 20);box-shadow: 0px 0px 32px 8px rgb(18, 20, 20), 0px 0px 4px 1px rgb(18, 20, 20) inset;}.reactor-container-inner {height: 238px; width: 238px; background-color: rgb(22, 26, 27);;box-shadow: 0px 0px 4px 1px #52FEFE;}.circle {border-radius: 50%;}.abs-center {position: absolute;top: 0;right: 0;bottom: 0;left: 0;margin: auto;}.core-inner {width: 70px;height: 70px;border: 5px solid #1B4E5F;background-color: #FFFFFF;box-shadow: 0px 0px 7px 5px #52FEFE, 0px 0px 10px 10px #52FEFE inset;}.core-outer {width: 120px;height: 120px;border: 1px solid #52FEFE;background-color: #FFFFFF;box-shadow: 0px 0px 2px 1px #52FEFE, 0px 0px 10px 5px #52FEFE inset;}.core-wrapper {width: 180px;height: 180px;background-color: #073c4b;box-shadow: 0px 0px 5px 4px #52FEFE, 0px 0px 6px 2px #52FEFE inset;}.tunnel {width: 220px;height: 220px;background-color: #FFFFFF;box-shadow: 0px 0px 5px 1px #52FEFE, 0px 0px 5px 4px #52FEFE inset;}.coil-container {position: relative;width: 100%;height: 100%;animation: 3s infinite linear reactor-anim;}.coil {position: absolute;width: 30px;height: 20px;top: calc(50% - 110px);left: calc(50% - 15px);transform-origin: 15px 110px;background-color:#073c4b;box-shadow: 0px 0px 5px #52FEFE inset;}.coil-1 {transform: rotate(0deg);}.coil-2 {transform: rotate(45deg);}.coil-3 {transform: rotate(90deg);}.coil-4 {transform: rotate(135deg);}.coil-5 {transform: rotate(180deg);}.coil-6 {transform: rotate(225deg);}.coil-7 {transform: rotate(270deg);}.coil-8 { transform: rotate(315deg);}@keyframes reactor-anim{from {transform: rotate(0deg);}to {transform: rotate(360deg);}}</style></body></html>$

Answered by Anonymous

The Indian System................!!!

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Let f : W → W be defined as f (n) = n – 1, if n is odd and f (n) = n + 1, if n is even. Show that f is invertible. Find the inverse of f. Here, W is the set of all whole numbers.​

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Let f : W → W be defined as f (n) = n – 1, if n is odd and f (n) = n + 1, if n is even. Show that f is invertible. Find the inverse of f. Here, W is the set of all whole numbers.