Example 2

Find the inverse, , of the function and determine the domain value(s) over which the inverse exists.
  1. Switch the domain and function variables, and then rename as .
  2. Rewrite the possible inverse in a form that can be solved for .
  3. Solve for using the quadratic formula.
  4. Determine the domain of .
  5. Determine the range of .
  6. Determine the domain of .
  7. Determine whether exhibits one-to-one correspondence.
  8. Determine the parts of its domain over which exhibits one-to-one correspondence.
  9. Determine the range of .
  10. Match domains to ranges to find the inverse(s) of .
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