1. [n]  (math) one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the inverse of 7 is 1/7
2. [n]  something inverted in sequence or character or effect; "when the direct approach failed he tried the inverse"
3. [adj]  reversed (turned backward) in order or nature or effect
4. [adj]  (mathematics) varying in a manner opposite to that of another quantity; "a term is in inverse proportion to another term if it increases (or decreases) as the other decreases (or increases)"
5. [adj]  inversely related; "1/2 is the inverse of 2"

1. \In*verse"\, a. [L. inversus, p. p. of invertere: cf. F.
   inverse. See {Invert}.]
   1. Opposite in order, relation, or effect; reversed;
      inverted; reciprocal; -- opposed to {direct}.
   2. (Bot.) Inverted; having a position or mode of attachment
      the reverse of that which is usual.
   3. (Math.) Opposite in nature and effect; -- said with
      reference to any two operations, which, when both are
      performed in succession upon any quantity, reproduce that
      quantity; as, multiplication is the inverse operation to
      division. The symbol of an inverse operation is the symbol
      of the direct operation with -1 as an index. Thus sin-1 x
      means the arc whose sine is x.
   {Inverse figures} (Geom.), two figures, such that each point
      of either figure is inverse to a corresponding point in
      the order figure.
   {Inverse points} (Geom.), two points lying on a line drawn
      from the center of a fixed circle or sphere, and so
      related that the product of their distances from the
      center of the circle or sphere is equal to the square of
      the radius.
   {Inverse}, or {Reciprocal}, {ratio} (Math.), the ratio of the
      reciprocals of two quantities.
   {Inverse}, or {Reciprocal, {proportion}, an equality between
      a direct ratio and a reciprocal ratio; thus, 4 : 2 : : 1/3
      : 1/6, or 4 : 2 : : 3 : 6, inversely.
   

2. \In"verse\, n.
   That which is inverse.
         Thus the course of human study is the inverse of the
         course of things in nature.              --Tatham.
   

Given a function, f : D -> C, a function g : C -> D is called a left inverse for f if for all d in D, g (f d) = d and a right inverse if, for all c in C, f (g c) = c and an inverse if both conditions hold. Only an injection has a left inverse, only a surjection has a right inverse and only a bijection has inverses. The inverse of f is often written as f with a -1 superscript.