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InverseFunction.md (511B)


      1 # Inverse Function
      2 
      3 L2
      4 
      5 **Definition:** The inverse function of f(x) is defined as f^-1(x) where f^-1(x) maps from the codomain of f(x) to the domain of f(x).
      6 
      7 As such, for a function to be invertible it must be a bijection.
      8 
      9 ## Finding
     10 
     11 The simplest way to find the inverse of a function is by swapping the y and x terms and then solving for y.
     12 
     13 Consider:
     14 
     15 $$
     16 f(x) = x^3 + 10
     17 \newline
     18 y = x^3 + 10
     19 \newline
     20 
     21 $$
     22 
     23 $$
     24 x = y^3 + 10
     25 \newline
     26 x+10 = y^3
     27 \newline
     28 y = \sqrt[3]{x+10}
     29 $$
     30 
     31 $$
     32 f'(x) = \sqrt[3]{x+10}
     33 $$
     34