{
localUrl: '../page/inverse_function.html',
arbitalUrl: 'https://arbital.com/p/inverse_function',
rawJsonUrl: '../raw/4sn.json',
likeableId: '2845',
likeableType: 'page',
myLikeValue: '0',
likeCount: '2',
dislikeCount: '0',
likeScore: '2',
individualLikes: [
'EricBruylant',
'EricRogstad'
],
pageId: 'inverse_function',
edit: '5',
editSummary: '',
prevEdit: '4',
currentEdit: '5',
wasPublished: 'true',
type: 'wiki',
title: 'Inverse function',
clickbait: 'The inverse of a function returns an input of the original function when fed the original's corresponding output.',
textLength: '658',
alias: 'inverse_function',
externalUrl: '',
sortChildrenBy: 'likes',
hasVote: 'false',
voteType: '',
votesAnonymous: 'false',
editCreatorId: 'DylanHendrickson',
editCreatedAt: '2016-07-07 17:47:27',
pageCreatorId: 'MichaelCohen',
pageCreatedAt: '2016-06-24 07:54:39',
seeDomainId: '0',
editDomainId: 'AlexeiAndreev',
submitToDomainId: '0',
isAutosave: 'false',
isSnapshot: 'false',
isLiveEdit: 'true',
isMinorEdit: 'false',
indirectTeacher: 'false',
todoCount: '0',
isEditorComment: 'false',
isApprovedComment: 'true',
isResolved: 'false',
snapshotText: '',
anchorContext: '',
anchorText: '',
anchorOffset: '0',
mergedInto: '',
isDeleted: 'false',
viewCount: '75',
text: 'If a function $g$ is the inverse of a function $f$, then $g$ undoes $f$, and $f$ undoes $g$. In other words, $g(f(x)) = x$ and $f(g(y)) = y$. An inverse function takes as its [3js domain] the [3lm range] of the original function, and the [3lm range] of the inverse function is the [3js domain] of the original. To put that another way, if $f$ maps $A$ onto $B$, then $g$ maps $B$ back onto $A$. To indicate the inverse of a function $f$, we write $f^{-1}$.\n\n## Examples ##\n\n$$y=f(x) = x^3\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ x=f^{-1}(y) = y^{1/3}$$\n$$y=f(x) = e^x\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ x=f^{-1}(y) = ln(y)$$\n$$y=f(x) = x+4\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ x=f^{-1}(y) = y-4$$',
metaText: '',
isTextLoaded: 'true',
isSubscribedToDiscussion: 'false',
isSubscribedToUser: 'false',
isSubscribedAsMaintainer: 'false',
discussionSubscriberCount: '3',
maintainerCount: '3',
userSubscriberCount: '0',
lastVisit: '',
hasDraft: 'false',
votes: [],
voteSummary: 'null',
muVoteSummary: '0',
voteScaling: '0',
currentUserVote: '-2',
voteCount: '0',
lockedVoteType: '',
maxEditEver: '0',
redLinkCount: '0',
lockedBy: '',
lockedUntil: '',
nextPageId: '',
prevPageId: '',
usedAsMastery: 'false',
proposalEditNum: '0',
permissions: {
edit: {
has: 'false',
reason: 'You don't have domain permission to edit this page'
},
proposeEdit: {
has: 'true',
reason: ''
},
delete: {
has: 'false',
reason: 'You don't have domain permission to delete this page'
},
comment: {
has: 'false',
reason: 'You can't comment in this domain because you are not a member'
},
proposeComment: {
has: 'true',
reason: ''
}
},
summaries: {},
creatorIds: [
'MichaelCohen',
'EricBruylant',
'EricRogstad',
'DylanHendrickson'
],
childIds: [],
parentIds: [
'function'
],
commentIds: [
'4sq'
],
questionIds: [],
tagIds: [
'formal_definition_meta_tag'
],
relatedIds: [],
markIds: [],
explanations: [],
learnMore: [],
requirements: [],
subjects: [],
lenses: [],
lensParentId: '',
pathPages: [],
learnMoreTaughtMap: {},
learnMoreCoveredMap: {},
learnMoreRequiredMap: {},
editHistory: {},
domainSubmissions: {},
answers: [],
answerCount: '0',
commentCount: '0',
newCommentCount: '0',
linkedMarkCount: '0',
changeLogs: [
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16020',
pageId: 'inverse_function',
userId: 'DylanHendrickson',
edit: '0',
type: 'newAlias',
createdAt: '2016-07-07 17:47:27',
auxPageId: '',
oldSettingsValue: 'inverse',
newSettingsValue: 'inverse_function'
},
{
likeableId: '3004',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '1',
dislikeCount: '0',
likeScore: '1',
individualLikes: [],
id: '16021',
pageId: 'inverse_function',
userId: 'DylanHendrickson',
edit: '5',
type: 'newEdit',
createdAt: '2016-07-07 17:47:27',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15133',
pageId: 'inverse_function',
userId: 'EricBruylant',
edit: '0',
type: 'newParent',
createdAt: '2016-07-02 23:27:49',
auxPageId: 'function',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15131',
pageId: 'inverse_function',
userId: 'EricBruylant',
edit: '0',
type: 'deleteParent',
createdAt: '2016-07-02 23:27:43',
auxPageId: 'math',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15129',
pageId: 'inverse_function',
userId: 'EricBruylant',
edit: '0',
type: 'newParent',
createdAt: '2016-07-02 23:27:22',
auxPageId: 'math',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15127',
pageId: 'inverse_function',
userId: 'EricBruylant',
edit: '0',
type: 'deleteParent',
createdAt: '2016-07-02 23:27:12',
auxPageId: 'function',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '14739',
pageId: 'inverse_function',
userId: 'MichaelCohen',
edit: '4',
type: 'newEdit',
createdAt: '2016-06-28 23:26:02',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '14589',
pageId: 'inverse_function',
userId: 'EricRogstad',
edit: '3',
type: 'newEdit',
createdAt: '2016-06-25 06:53:51',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: 'minor rewording'
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '14570',
pageId: 'inverse_function',
userId: 'EricBruylant',
edit: '2',
type: 'newEdit',
createdAt: '2016-06-24 17:27:50',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '14569',
pageId: 'inverse_function',
userId: 'EricBruylant',
edit: '0',
type: 'newTag',
createdAt: '2016-06-24 17:16:11',
auxPageId: 'formal_definition_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '14568',
pageId: 'inverse_function',
userId: 'EricBruylant',
edit: '0',
type: 'newParent',
createdAt: '2016-06-24 17:15:56',
auxPageId: 'function',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '14565',
pageId: 'inverse_function',
userId: 'MichaelCohen',
edit: '1',
type: 'newEdit',
createdAt: '2016-06-24 07:54:39',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
}
],
feedSubmissions: [],
searchStrings: {},
hasChildren: 'false',
hasParents: 'true',
redAliases: {},
improvementTagIds: [],
nonMetaTagIds: [],
todos: [],
slowDownMap: 'null',
speedUpMap: 'null',
arcPageIds: 'null',
contentRequests: {}
}