Honors Algebra 2: Inverse Function Worksheet

  1. Given \( f(x) = 2x + 6 \) and \( \displaystyle g(x) = \frac{4 - 5x}{3}\), find...
    1. The inverse of \( \displaystyle f(g(x)) \).
      2. Solution

      \( \displaystyle \frac{26 - 3x}{10} \)

    2. \( \displaystyle f^{-1}\left( g(x) \right) \).
      3. Solution

      \( \displaystyle \frac{-5x - 14}{6} \)

    3. \( \displaystyle f\left( g^{-1}(x) \right) \).
      4. Solution

      \( \displaystyle \frac{38-6x}{5} \)

    4. \( \displaystyle g\left( f^{-1}(x) \right) \).
      5. Solution

      \( \displaystyle \frac{38 - 5x}{6} \)

    5. \( \displaystyle g\left( f(x) \right) \).
      6. Solution

      \( \displaystyle \frac{-26 - 10x}{3} \)

    6. \( \displaystyle f\left( f^{-1}(x) \right) \).
      7. Solution

      \( \displaystyle x \)