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Function

Function

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• 1. I N V E R S E FUNCTIONS
• 2. DOMAIN OF f RANGE OF f RANGE OF f -1 DOMAIN OF f - -1 x x y y 1 TO 1 FUNCTION f(x) = y f -1 (y) = x Dom (f) =Ran ( f -1 ) Ran (f) =Dom (f -1 ) INVERSE FUNCTION
• 3. EXAMPLE 1
• GIVEN THAT THE FOLLOWING
• FUNCTIONS HAS DOMAIN R. DETERMINE
• WHETHER INVERSE FUNCTION EXIST
• OR NOT.
• i. ii.
• iii. iv.
• v. vi.
• 4.
• YES ( 1 TO 1 FUNCTION )
• NO ( MANY TO 1 RELATION )
• NO ( MANY TO 1 RELATION )
• YES ( 1 TO 1 FUNCTION )
• NO ( MANY TO 1 RELATION )
• YES ( 1 TO 1 FUNCTION )
• 5. EXAMPLE 2
• DETERMINE WHICH OF THE FOLLOWING
• FUNCTION HAS INVERSE FUNCTIONS IN
• THE SPECIFIED DOMAINS.
• i.
• ii.
• iii.
• iv.
• v.
• 6.
• YES ( 1 TO 1 FUNCTION )
• YES ( 1 TO 1 FUNCTION )
• YES ( 1 TO 1 FUNCTION )
• YES ( 1 TO 1 FUNCTION )
• NO ( MANY TO 1 FUNCTION )
• 7. EXAMPLE 3
• DETERMINE THE DOMAIN OF THE FUNCTION SO THAT AN INVERSE FUNCTION EXISTS.
• 8. EXAMPLE 4
• FIND THE INVERSE FUNCTION FOR THE
• FOLLOWING FUNCTIONS.
• i.
• ii.
• iii.
• 9.
• i.
• ii.
• 10.
• iii.
• 11. EXAMPLE 5
• DETERMINE THE RANGE OF FIND
• THE INVERSE FUNCTION FOR THE
• FOLLOWING FUNCTIONS AND STATE ITS
• DOMAIN AND RANGE.
• i.
• ii.
• iii.
• 12.
• i.
Dom (f) =Ran ( f -1 ) Ran (f) =Dom (f -1 )
• 13.
• ii.
• 14.
• iii.
• 15.
• IF IS 1-1 FUNCTION, THE GRAPHS
• AND ARE REFLECTIONS
• OF EACH OTHER IN THE LINE
x y (m,n) (n,m)
• 16. EXAMPLE 6
• GIVEN THAT
• FIND ITS INVERSE AND SKETCH BOTH GRAPHS IN THE SAME DIAGRAM.
• 17. x y (3,-4) (-4,3) INVERSE FUNCTION