Question 204173
if  we  use,,y=2x,,,this  is  well  defined, on a  x-y  coordinate  plane, y rises  twice as  fast  as  x moves  to  right.
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g(x) =2x  or h(x) =2x,,,,,mean  the  same  thing,,,except the  axis  is  now  g(x),,or h(x).
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The  advantage  of  using  functional  notation  is  that  different  items  can  be  differentiated,  and  still  shown  to  be  a  function  of  x.
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If  we  had  a  cost,  we  might  use c(x).  If  we  just  used  "c", it  might  not  be  clear  that  it is  a  function  of  x.
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Some  problems have  multiple functional  relationships, we  could  use  y(1), y(2), and  y(3), ( and  then use  a  let y(1) = cost, y(2) = quantity, etc),  but it  might  be  easier to  just  use  c(x), q(x), t(x), etc to differentiate.
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The  composite functions  of  higher math often  use  h(x) and  g(x), in  combination,,defining  which  comes  first, and  which  is  second. The  substitution is  bad  enough,  but  using  y's  would  make  it  worse.
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In  summary,  feel  free  to  immediately use "y ="  instead  of  "h(x)",
if  it  clarified  the  problem.