Chapter 2 Section 5

Notes

Linguistic Mapping Exercises

Knowledge Checks

  1. Determine whether the function \(f=\{(1,3),(2,5),(-3,6),(4,3)\}\) is invertible. If not, remove points so that it is. In either case, write out the inverse.
  2. Take \(f\) to be an invertible function with domain \((4,10]\) and range \((-4,3)\). Determine the domain and range of the inverse of \(f\).
  3. Sketch \(f|_{(-3,-2)\cup[0,1]}\) where \(f(x)=x^2.\) Then sketch the inverse of \(f|_{(-3,-2)\cup[0,1]}\) and write a formula for it.
  4. Find the inverse of \(f(x)=3(x-2)^3+1\). Determine the domain and range of \(f\) and its inverse.
  5. Find the inverse of \(f(x)=\frac{x-3}{2x+4}\). Determine the domain and range of \(f\) and its inverse.
  6. Find the inverse of \(f(x)=\sqrt{x-2}+1.\) Determine the domain and range of \(f\) and its inverse.

Remember, do the knowledge checks before checking the solutions.

Practice Problems

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