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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