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MAT135H1 Study Guide - Inverse Function, Inverse Relation


Department
Mathematics
Course Code
MAT135H1
Professor
all

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Inverse'Functions'
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Knowledge'Summary:'
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Definition:!The!inverse!of!a!function!is!the!set!of!ordered!pairs!obtained!by!interchanging!the!first!and!
second!elements!of!each!pair!in!the!original!function.!Should!the!inverse!of!function!f(x)!also!be!a!function,!
this!inverse!function!is!denoted!by!f?1!(x).!!!
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One?to?One!Function:!A!function!is!a!one?to?one!function!if!and!only!if!each!second!element!corresponds!
to!one!and!only!one!first!element!(i.e.!each!x!and!y!value!is!used!only!once)!
Use!the!horizontal!line!test!to!determine!if!a!function!is!a!one?to?one!function!
If!any!horizontal!line!intersects!your!original!function!in!only!one!location,!your!function!will!be!a!
one?to?one!function!and!its!inverse!will!also!be!a!function!
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Three!Solutions:!
1) Interchange!ordered!pairs:!if!your!function!is!defined!as!a!list!of!ordered!pairs,!simply!interchange!
the!x!and!y!values!
2) Solve!algebraically:!solve!for!an!inverse!relation!algebraically:!!
a. Set!the!function!=!y!
b. Swap!the!x!and!y!variables!
c. Solve!for!y!
3) Graph:!the!graph!of!an!inverse!relation!is!the!reflection!of!the!original!graph!over!the!identity!line,!
y=x.!!
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Past'Test'Questions:'
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Questions:''
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1)!Nov’!03!question!3!
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