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2- Inverse Functions

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Department
Mathematics
Course Code
MAT135H1
Professor
all

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Description
Inverse  Functions     Knowledge  Summary:     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  (x).      -­‐1   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  t est  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     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  
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