Honors Algebra 2: Inverse Function Worksheet

  1. Given the graph of the following relation:
    graph
    1. Is the relation a function?
      2. Solution Yes
    2. Is the inverse of the relation a function?
      3. Solution Yes
    3. Sketch the inverse of the relation on the same graph as the original relation.
      4. Solution graph
  2. Given the graph of the following relation:
    graph
    1. Is the relation a function?
      2. Solution Yes
    2. Is the inverse of the relation a function?
      3. Solution No
    3. Sketch the inverse of the relation on the same graph as the original relation.
      4. Solution graph
  3. Given the graph of the following relation:
    graph
    1. Is the relation a function?
      2. Solution Yes
    2. Is the inverse of the relation a function?
      3. Solution No
    3. Sketch the inverse of the relation on the same graph as the original relation.
      4. Solution graph
  4. Given the graph of the following relation:
    graph
    1. Is the relation a function?
      2. Solution No
    2. Is the inverse of the relation a function?
      3. Solution No
    3. Sketch the inverse of the relation on the same graph as the original relation.
      4. Solution The graph of the inverse looks exactly like the graph of the original relation.
  5. Given \( f(x) = 3x + 5\), find \( f^{-1}(x)\)
    6. Solution \( \displaystyle f^{-1}(x) = \frac{x - 5}{3}\)
  6. Given \( \displaystyle f(x) = \frac{x}{2} - \frac{1}{4}\), find \( f^{-1}(x)\)
    7. Solution \( \displaystyle f^{-1}(x) = \frac{4x +1}{2} \)
  7. Given the function \( f(x) = \{ (2, 1), (3, 2), (1, 3) \} \), find \( f^{-1} \left( f \left( f (1) \right) \right) \)
    8. Solution 3
  8. Given \( f(x) = 3x + 6\) and \(g(x) = 2x - 5\), find the inverse of \( f \left( g(x) \right) \)
    9. Solution \( \displaystyle \frac{x}{6} + \frac{3}{2}\)
  9. Given \( f(x) = .81375x - .27963\), find \( f \left( f \left( f^{-1} \left( f^{-1}(x) \right) \right) \right) \)
    10. Solution \(x\)
  10. Given \( f(x) = 8x - 4\), find and simplify \(f^{-1}(16a + 12)\)
    11. Solution \(2a + 2\).
  11. Given the graph of \(y = f(x) \) is moved 4 units to the right to make the graph of \(y = g(x) \), what would the graph of \(y = g^{-1}(x)\) look like?
    12. Solution It would look like the graph of \(y = f (x)\) flipped over the line \(y = x\), and moved up 4 units.